Question 27800: All Nonzero Prime Residues Pair with Inverses, with a Special p=2 Case

Original question and givens

Use prime modulus p=97. Give (p, all_inverse_pairs, self_inverse_residues, distinct_cancelling_pairs, self_inverse_scope, factorial_residue, Wilson_congruence).

• G001 — Use prime modulus p=97. Give (p, all_inverse_pairs, self_inverse_residues, distinct_cancelling_pairs, self_inverse_scope, factorial_residue, Wilson_congruence).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-wilson-theorem

Step-by-step derivation

source roles = [wilson-prime-inverse-pairing]

derived = [[p, all_inverse_pairs, self_inverse_residues, distinct_cancelling_pairs, self_inverse_scope, factorial_residue, Wilson_congruence]]

source roles = [97, 1]

derived = [1, 1]

source roles = [97, 2]

derived = [49, 1]

source roles = [97, 3]

derived = [65, 1]

source roles = [97, 4]

derived = [73, 1]

source roles = [97, 5]

derived = [39, 1]

source roles = [97, 6]

derived = [81, 1]

source roles = [97, 7]

derived = [14, 1]

source roles = [97, 8]

derived = [85, 1]

source roles = [97, 9]

derived = [54, 1]

source roles = [97, 10]

derived = [68, 1]

source roles = [97, 11]

derived = [53, 1]

source roles = [97, 12]

derived = [89, 1]

source roles = [97, 13]

derived = [15, 1]

source roles = [97, 14]

derived = [7, 1]

source roles = [97, 15]

derived = [13, 1]

source roles = [97, 16]

derived = [91, 1]

source roles = [97, 17]

derived = [40, 1]

source roles = [97, 18]

derived = [27, 1]

source roles = [97, 19]

derived = [46, 1]

source roles = [97, 20]

derived = [34, 1]

source roles = [97, 21]

derived = [37, 1]

source roles = [97, 22]

derived = [75, 1]

source roles = [97, 23]

derived = [38, 1]

source roles = [97, 24]

derived = [93, 1]

source roles = [97, 25]

derived = [66, 1]

source roles = [97, 26]

derived = [56, 1]

source roles = [97, 27]

derived = [18, 1]

source roles = [97, 28]

derived = [52, 1]

source roles = [97, 29]

derived = [87, 1]

source roles = [97, 30]

derived = [55, 1]

source roles = [97, 31]

derived = [72, 1]

source roles = [97, 32]

derived = [94, 1]

source roles = [97, 33]

derived = [50, 1]

source roles = [97, 34]

derived = [20, 1]

source roles = [97, 35]

derived = [61, 1]

source roles = [97, 36]

derived = [62, 1]

source roles = [97, 37]

derived = [21, 1]

source roles = [97, 38]

derived = [23, 1]

source roles = [97, 39]

derived = [5, 1]

source roles = [97, 40]

derived = [17, 1]

source roles = [97, 41]

derived = [71, 1]

source roles = [97, 42]

derived = [67, 1]

source roles = [97, 43]

derived = [88, 1]

source roles = [97, 44]

derived = [86, 1]

source roles = [97, 45]

derived = [69, 1]

source roles = [97, 46]

derived = [19, 1]

source roles = [97, 47]

derived = [64, 1]

source roles = [97, 48]

derived = [95, 1]

source roles = [97, 49]

derived = [2, 1]

source roles = [97, 50]

derived = [33, 1]

source roles = [97, 51]

derived = [78, 1]

source roles = [97, 52]

derived = [28, 1]

source roles = [97, 53]

derived = [11, 1]

source roles = [97, 54]

derived = [9, 1]

source roles = [97, 55]

derived = [30, 1]

source roles = [97, 56]

derived = [26, 1]

source roles = [97, 57]

derived = [80, 1]

source roles = [97, 58]

derived = [92, 1]

source roles = [97, 59]

derived = [74, 1]

source roles = [97, 60]

derived = [76, 1]

source roles = [97, 61]

derived = [35, 1]

source roles = [97, 62]

derived = [36, 1]

source roles = [97, 63]

derived = [77, 1]

source roles = [97, 64]

derived = [47, 1]

source roles = [97, 65]

derived = [3, 1]

source roles = [97, 66]

derived = [25, 1]

source roles = [97, 67]

derived = [42, 1]

source roles = [97, 68]

derived = [10, 1]

source roles = [97, 69]

derived = [45, 1]

source roles = [97, 70]

derived = [79, 1]

source roles = [97, 71]

derived = [41, 1]

source roles = [97, 72]

derived = [31, 1]

source roles = [97, 73]

derived = [4, 1]

source roles = [97, 74]

derived = [59, 1]

source roles = [97, 75]

derived = [22, 1]

source roles = [97, 76]

derived = [60, 1]

source roles = [97, 77]

derived = [63, 1]

source roles = [97, 78]

derived = [51, 1]

source roles = [97, 79]

derived = [70, 1]

source roles = [97, 80]

derived = [57, 1]

source roles = [97, 81]

derived = [6, 1]

source roles = [97, 82]

derived = [84, 1]

source roles = [97, 83]

derived = [90, 1]

source roles = [97, 84]

derived = [82, 1]

source roles = [97, 85]

derived = [8, 1]

source roles = [97, 86]

derived = [44, 1]

source roles = [97, 87]

derived = [29, 1]

source roles = [97, 88]

derived = [43, 1]

source roles = [97, 89]

derived = [12, 1]

source roles = [97, 90]

derived = [83, 1]

source roles = [97, 91]

derived = [16, 1]

source roles = [97, 92]

derived = [58, 1]

source roles = [97, 93]

derived = [24, 1]

source roles = [97, 94]

derived = [32, 1]

source roles = [97, 95]

derived = [48, 1]

source roles = [97, 96]

derived = [96, 1]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product1 := mul(1, 1)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product1 = 1

source roles = [Wilson ORIGINAL prime factorial, 97, 1, 1, 1]

derived = [0, 1, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product2 := mul(1, 2)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product2 = 2

source roles = [Wilson ORIGINAL prime factorial, 97, 2, 1, 2]

derived = [0, 2, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product3 := mul(2, 3)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product3 = 6

source roles = [Wilson ORIGINAL prime factorial, 97, 3, 2, 6]

derived = [0, 6, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product4 := mul(6, 4)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product4 = 24

source roles = [Wilson ORIGINAL prime factorial, 97, 4, 6, 24]

derived = [0, 24, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product5 := mul(24, 5)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product5 = 120

source roles = [Wilson ORIGINAL prime factorial, 97, 5, 24, 120]

derived = [1, 23, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product6 := mul(23, 6)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product6 = 138

source roles = [Wilson ORIGINAL prime factorial, 97, 6, 23, 138]

derived = [1, 41, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product7 := mul(41, 7)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product7 = 287

source roles = [Wilson ORIGINAL prime factorial, 97, 7, 41, 287]

derived = [2, 93, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product8 := mul(93, 8)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product8 = 744

source roles = [Wilson ORIGINAL prime factorial, 97, 8, 93, 744]

derived = [7, 65, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product9 := mul(65, 9)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product9 = 585

source roles = [Wilson ORIGINAL prime factorial, 97, 9, 65, 585]

derived = [6, 3, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product10 := mul(3, 10)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product10 = 30

source roles = [Wilson ORIGINAL prime factorial, 97, 10, 3, 30]

derived = [0, 30, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product11 := mul(30, 11)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product11 = 330

source roles = [Wilson ORIGINAL prime factorial, 97, 11, 30, 330]

derived = [3, 39, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product12 := mul(39, 12)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product12 = 468

source roles = [Wilson ORIGINAL prime factorial, 97, 12, 39, 468]

derived = [4, 80, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product13 := mul(80, 13)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product13 = 1040

source roles = [Wilson ORIGINAL prime factorial, 97, 13, 80, 1040]

derived = [10, 70, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product14 := mul(70, 14)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product14 = 980

source roles = [Wilson ORIGINAL prime factorial, 97, 14, 70, 980]

derived = [10, 10, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product15 := mul(10, 15)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product15 = 150

source roles = [Wilson ORIGINAL prime factorial, 97, 15, 10, 150]

derived = [1, 53, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product16 := mul(53, 16)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product16 = 848

source roles = [Wilson ORIGINAL prime factorial, 97, 16, 53, 848]

derived = [8, 72, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product17 := mul(72, 17)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product17 = 1224

source roles = [Wilson ORIGINAL prime factorial, 97, 17, 72, 1224]

derived = [12, 60, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product18 := mul(60, 18)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product18 = 1080

source roles = [Wilson ORIGINAL prime factorial, 97, 18, 60, 1080]

derived = [11, 13, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product19 := mul(13, 19)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product19 = 247

source roles = [Wilson ORIGINAL prime factorial, 97, 19, 13, 247]

derived = [2, 53, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product20 := mul(53, 20)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product20 = 1060

source roles = [Wilson ORIGINAL prime factorial, 97, 20, 53, 1060]

derived = [10, 90, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product21 := mul(90, 21)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product21 = 1890

source roles = [Wilson ORIGINAL prime factorial, 97, 21, 90, 1890]

derived = [19, 47, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product22 := mul(47, 22)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product22 = 1034

source roles = [Wilson ORIGINAL prime factorial, 97, 22, 47, 1034]

derived = [10, 64, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product23 := mul(64, 23)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product23 = 1472

source roles = [Wilson ORIGINAL prime factorial, 97, 23, 64, 1472]

derived = [15, 17, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product24 := mul(17, 24)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product24 = 408

source roles = [Wilson ORIGINAL prime factorial, 97, 24, 17, 408]

derived = [4, 20, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product25 := mul(20, 25)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product25 = 500

source roles = [Wilson ORIGINAL prime factorial, 97, 25, 20, 500]

derived = [5, 15, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product26 := mul(15, 26)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product26 = 390

source roles = [Wilson ORIGINAL prime factorial, 97, 26, 15, 390]

derived = [4, 2, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product27 := mul(2, 27)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product27 = 54

source roles = [Wilson ORIGINAL prime factorial, 97, 27, 2, 54]

derived = [0, 54, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product28 := mul(54, 28)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product28 = 1512

source roles = [Wilson ORIGINAL prime factorial, 97, 28, 54, 1512]

derived = [15, 57, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product29 := mul(57, 29)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product29 = 1653

source roles = [Wilson ORIGINAL prime factorial, 97, 29, 57, 1653]

derived = [17, 4, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product30 := mul(4, 30)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product30 = 120

source roles = [Wilson ORIGINAL prime factorial, 97, 30, 4, 120]

derived = [1, 23, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product31 := mul(23, 31)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product31 = 713

source roles = [Wilson ORIGINAL prime factorial, 97, 31, 23, 713]

derived = [7, 34, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product32 := mul(34, 32)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product32 = 1088

source roles = [Wilson ORIGINAL prime factorial, 97, 32, 34, 1088]

derived = [11, 21, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product33 := mul(21, 33)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product33 = 693

source roles = [Wilson ORIGINAL prime factorial, 97, 33, 21, 693]

derived = [7, 14, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product34 := mul(14, 34)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product34 = 476

source roles = [Wilson ORIGINAL prime factorial, 97, 34, 14, 476]

derived = [4, 88, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product35 := mul(88, 35)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product35 = 3080

source roles = [Wilson ORIGINAL prime factorial, 97, 35, 88, 3080]

derived = [31, 73, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product36 := mul(73, 36)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product36 = 2628

source roles = [Wilson ORIGINAL prime factorial, 97, 36, 73, 2628]

derived = [27, 9, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product37 := mul(9, 37)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product37 = 333

source roles = [Wilson ORIGINAL prime factorial, 97, 37, 9, 333]

derived = [3, 42, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product38 := mul(42, 38)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product38 = 1596

source roles = [Wilson ORIGINAL prime factorial, 97, 38, 42, 1596]

derived = [16, 44, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product39 := mul(44, 39)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product39 = 1716

source roles = [Wilson ORIGINAL prime factorial, 97, 39, 44, 1716]

derived = [17, 67, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product40 := mul(67, 40)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product40 = 2680

source roles = [Wilson ORIGINAL prime factorial, 97, 40, 67, 2680]

derived = [27, 61, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product41 := mul(61, 41)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product41 = 2501

source roles = [Wilson ORIGINAL prime factorial, 97, 41, 61, 2501]

derived = [25, 76, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product42 := mul(76, 42)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product42 = 3192

source roles = [Wilson ORIGINAL prime factorial, 97, 42, 76, 3192]

derived = [32, 88, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product43 := mul(88, 43)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product43 = 3784

source roles = [Wilson ORIGINAL prime factorial, 97, 43, 88, 3784]

derived = [39, 1, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product44 := mul(1, 44)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product44 = 44

source roles = [Wilson ORIGINAL prime factorial, 97, 44, 1, 44]

derived = [0, 44, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product45 := mul(44, 45)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product45 = 1980

source roles = [Wilson ORIGINAL prime factorial, 97, 45, 44, 1980]

derived = [20, 40, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product46 := mul(40, 46)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product46 = 1840

source roles = [Wilson ORIGINAL prime factorial, 97, 46, 40, 1840]

derived = [18, 94, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product47 := mul(94, 47)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product47 = 4418

source roles = [Wilson ORIGINAL prime factorial, 97, 47, 94, 4418]

derived = [45, 53, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product48 := mul(53, 48)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product48 = 2544

source roles = [Wilson ORIGINAL prime factorial, 97, 48, 53, 2544]

derived = [26, 22, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product49 := mul(22, 49)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product49 = 1078

source roles = [Wilson ORIGINAL prime factorial, 97, 49, 22, 1078]

derived = [11, 11, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product50 := mul(11, 50)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product50 = 550

source roles = [Wilson ORIGINAL prime factorial, 97, 50, 11, 550]

derived = [5, 65, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product51 := mul(65, 51)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product51 = 3315

source roles = [Wilson ORIGINAL prime factorial, 97, 51, 65, 3315]

derived = [34, 17, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product52 := mul(17, 52)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product52 = 884

source roles = [Wilson ORIGINAL prime factorial, 97, 52, 17, 884]

derived = [9, 11, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product53 := mul(11, 53)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product53 = 583

source roles = [Wilson ORIGINAL prime factorial, 97, 53, 11, 583]

derived = [6, 1, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product54 := mul(1, 54)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product54 = 54

source roles = [Wilson ORIGINAL prime factorial, 97, 54, 1, 54]

derived = [0, 54, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product55 := mul(54, 55)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product55 = 2970

source roles = [Wilson ORIGINAL prime factorial, 97, 55, 54, 2970]

derived = [30, 60, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product56 := mul(60, 56)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product56 = 3360

source roles = [Wilson ORIGINAL prime factorial, 97, 56, 60, 3360]

derived = [34, 62, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product57 := mul(62, 57)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product57 = 3534

source roles = [Wilson ORIGINAL prime factorial, 97, 57, 62, 3534]

derived = [36, 42, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product58 := mul(42, 58)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product58 = 2436

source roles = [Wilson ORIGINAL prime factorial, 97, 58, 42, 2436]

derived = [25, 11, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product59 := mul(11, 59)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product59 = 649

source roles = [Wilson ORIGINAL prime factorial, 97, 59, 11, 649]

derived = [6, 67, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product60 := mul(67, 60)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product60 = 4020

source roles = [Wilson ORIGINAL prime factorial, 97, 60, 67, 4020]

derived = [41, 43, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product61 := mul(43, 61)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product61 = 2623

source roles = [Wilson ORIGINAL prime factorial, 97, 61, 43, 2623]

derived = [27, 4, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product62 := mul(4, 62)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product62 = 248

source roles = [Wilson ORIGINAL prime factorial, 97, 62, 4, 248]

derived = [2, 54, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product63 := mul(54, 63)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product63 = 3402

source roles = [Wilson ORIGINAL prime factorial, 97, 63, 54, 3402]

derived = [35, 7, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product64 := mul(7, 64)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product64 = 448

source roles = [Wilson ORIGINAL prime factorial, 97, 64, 7, 448]

derived = [4, 60, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product65 := mul(60, 65)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product65 = 3900

source roles = [Wilson ORIGINAL prime factorial, 97, 65, 60, 3900]

derived = [40, 20, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product66 := mul(20, 66)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product66 = 1320

source roles = [Wilson ORIGINAL prime factorial, 97, 66, 20, 1320]

derived = [13, 59, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product67 := mul(59, 67)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product67 = 3953

source roles = [Wilson ORIGINAL prime factorial, 97, 67, 59, 3953]

derived = [40, 73, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product68 := mul(73, 68)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product68 = 4964

source roles = [Wilson ORIGINAL prime factorial, 97, 68, 73, 4964]

derived = [51, 17, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product69 := mul(17, 69)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product69 = 1173

source roles = [Wilson ORIGINAL prime factorial, 97, 69, 17, 1173]

derived = [12, 9, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product70 := mul(9, 70)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product70 = 630

source roles = [Wilson ORIGINAL prime factorial, 97, 70, 9, 630]

derived = [6, 48, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product71 := mul(48, 71)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product71 = 3408

source roles = [Wilson ORIGINAL prime factorial, 97, 71, 48, 3408]

derived = [35, 13, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product72 := mul(13, 72)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product72 = 936

source roles = [Wilson ORIGINAL prime factorial, 97, 72, 13, 936]

derived = [9, 63, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product73 := mul(63, 73)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product73 = 4599

source roles = [Wilson ORIGINAL prime factorial, 97, 73, 63, 4599]

derived = [47, 40, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product74 := mul(40, 74)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product74 = 2960

source roles = [Wilson ORIGINAL prime factorial, 97, 74, 40, 2960]

derived = [30, 50, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product75 := mul(50, 75)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product75 = 3750

source roles = [Wilson ORIGINAL prime factorial, 97, 75, 50, 3750]

derived = [38, 64, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product76 := mul(64, 76)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product76 = 4864

source roles = [Wilson ORIGINAL prime factorial, 97, 76, 64, 4864]

derived = [50, 14, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product77 := mul(14, 77)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product77 = 1078

source roles = [Wilson ORIGINAL prime factorial, 97, 77, 14, 1078]

derived = [11, 11, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product78 := mul(11, 78)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product78 = 858

source roles = [Wilson ORIGINAL prime factorial, 97, 78, 11, 858]

derived = [8, 82, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product79 := mul(82, 79)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product79 = 6478

source roles = [Wilson ORIGINAL prime factorial, 97, 79, 82, 6478]

derived = [66, 76, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product80 := mul(76, 80)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product80 = 6080

source roles = [Wilson ORIGINAL prime factorial, 97, 80, 76, 6080]

derived = [62, 66, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product81 := mul(66, 81)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product81 = 5346

source roles = [Wilson ORIGINAL prime factorial, 97, 81, 66, 5346]

derived = [55, 11, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product82 := mul(11, 82)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product82 = 902

source roles = [Wilson ORIGINAL prime factorial, 97, 82, 11, 902]

derived = [9, 29, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product83 := mul(29, 83)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product83 = 2407

source roles = [Wilson ORIGINAL prime factorial, 97, 83, 29, 2407]

derived = [24, 79, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product84 := mul(79, 84)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product84 = 6636

source roles = [Wilson ORIGINAL prime factorial, 97, 84, 79, 6636]

derived = [68, 40, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product85 := mul(40, 85)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product85 = 3400

source roles = [Wilson ORIGINAL prime factorial, 97, 85, 40, 3400]

derived = [35, 5, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product86 := mul(5, 86)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product86 = 430

source roles = [Wilson ORIGINAL prime factorial, 97, 86, 5, 430]

derived = [4, 42, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product87 := mul(42, 87)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product87 = 3654

source roles = [Wilson ORIGINAL prime factorial, 97, 87, 42, 3654]

derived = [37, 65, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product88 := mul(65, 88)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product88 = 5720

source roles = [Wilson ORIGINAL prime factorial, 97, 88, 65, 5720]

derived = [58, 94, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product89 := mul(94, 89)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product89 = 8366

source roles = [Wilson ORIGINAL prime factorial, 97, 89, 94, 8366]

derived = [86, 24, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product90 := mul(24, 90)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product90 = 2160

source roles = [Wilson ORIGINAL prime factorial, 97, 90, 24, 2160]

derived = [22, 26, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product91 := mul(26, 91)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product91 = 2366

source roles = [Wilson ORIGINAL prime factorial, 97, 91, 26, 2366]

derived = [24, 38, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product92 := mul(38, 92)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product92 = 3496

source roles = [Wilson ORIGINAL prime factorial, 97, 92, 38, 3496]

derived = [36, 4, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product93 := mul(4, 93)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product93 = 372

source roles = [Wilson ORIGINAL prime factorial, 97, 93, 4, 372]

derived = [3, 81, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product94 := mul(81, 94)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product94 = 7614

source roles = [Wilson ORIGINAL prime factorial, 97, 94, 81, 7614]

derived = [78, 48, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product95 := mul(48, 95)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product95 = 4560

source roles = [Wilson ORIGINAL prime factorial, 97, 95, 48, 4560]

derived = [47, 1, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product96 := mul(1, 96)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product96 = 96

source roles = [Wilson ORIGINAL prime factorial, 97, 96, 1, 96]

derived = [0, 96, Yes, Yes]

source roles = [97, [[1, 1], [2, 49], [3, 65], [4, 73], [5, 39], [6, 81], [7, 14], [8, 85], [9, 54], [10, 68], [11, 53], [12, 89], [13, 15], [14, 7], [15, 13], [16, 91], [17, 40], [18, 27], [19, 46], [20, 34], [21, 37], [22, 75], [23, 38], [24, 93], [25, 66], [26, 56], [27, 18], [28, 52], [29, 87], [30, 55], [31, 72], [32, 94], [33, 50], [34, 20], [35, 61], [36, 62], [37, 21], [38, 23], [39, 5], [40, 17], [41, 71], [42, 67], [43, 88], [44, 86], [45, 69], [46, 19], [47, 64], [48, 95], [49, 2], [50, 33], [51, 78], [52, 28], [53, 11], [54, 9], [55, 30], [56, 26], [57, 80], [58, 92], [59, 74], [60, 76], [61, 35], [62, 36], [63, 77], [64, 47], [65, 3], [66, 25], [67, 42], [68, 10], [69, 45], [70, 79], [71, 41], [72, 31], [73, 4], [74, 59], [75, 22], [76, 60], [77, 63], [78, 51], [79, 70], [80, 57], [81, 6], [82, 84], [83, 90], [84, 82], [85, 8], [86, 44], [87, 29], [88, 43], [89, 12], [90, 83], [91, 16], [92, 58], [93, 24], [94, 32], [95, 48], [96, 96]]]

derived = [[1, 96], [[2, 49, 1], [3, 65, 1], [4, 73, 1], [5, 39, 1], [6, 81, 1], [7, 14, 1], [8, 85, 1], [9, 54, 1], [10, 68, 1], [11, 53, 1], [12, 89, 1], [13, 15, 1], [16, 91, 1], [17, 40, 1], [18, 27, 1], [19, 46, 1], [20, 34, 1], [21, 37, 1], [22, 75, 1], [23, 38, 1], [24, 93, 1], [25, 66, 1], [26, 56, 1], [28, 52, 1], [29, 87, 1], [30, 55, 1], [31, 72, 1], [32, 94, 1], [33, 50, 1], [35, 61, 1], [36, 62, 1], [41, 71, 1], [42, 67, 1], [43, 88, 1], [44, 86, 1], [45, 69, 1], [47, 64, 1], [48, 95, 1], [51, 78, 1], [57, 80, 1], [58, 92, 1], [59, 74, 1], [60, 76, 1], [63, 77, 1], [70, 79, 1], [82, 84, 1], [83, 90, 1]], 96, Yes]

Reverse checks

• S290 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S289 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S288 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product96 with exact rational arithmetic, not rounded decimals.
• S287 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S286 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product95 with exact rational arithmetic, not rounded decimals.
• S285 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S284 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product94 with exact rational arithmetic, not rounded decimals.
• S283 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S282 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product93 with exact rational arithmetic, not rounded decimals.
• S281 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S280 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product92 with exact rational arithmetic, not rounded decimals.
• S279 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S278 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product91 with exact rational arithmetic, not rounded decimals.
• S277 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S276 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product90 with exact rational arithmetic, not rounded decimals.
• S275 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S274 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product89 with exact rational arithmetic, not rounded decimals.
• S273 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S272 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product88 with exact rational arithmetic, not rounded decimals.
• S271 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S270 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product87 with exact rational arithmetic, not rounded decimals.
• S269 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S268 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product86 with exact rational arithmetic, not rounded decimals.
• S267 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S266 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product85 with exact rational arithmetic, not rounded decimals.
• S265 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S264 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product84 with exact rational arithmetic, not rounded decimals.
• S263 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S262 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product83 with exact rational arithmetic, not rounded decimals.
• S261 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S260 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product82 with exact rational arithmetic, not rounded decimals.
• S259 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S258 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product81 with exact rational arithmetic, not rounded decimals.
• S257 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S256 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product80 with exact rational arithmetic, not rounded decimals.
• S255 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S254 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product79 with exact rational arithmetic, not rounded decimals.
• S253 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S252 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product78 with exact rational arithmetic, not rounded decimals.
• S251 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S250 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product77 with exact rational arithmetic, not rounded decimals.
• S249 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S248 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product76 with exact rational arithmetic, not rounded decimals.
• S247 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S246 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product75 with exact rational arithmetic, not rounded decimals.
• S245 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S244 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product74 with exact rational arithmetic, not rounded decimals.
• S243 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S242 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product73 with exact rational arithmetic, not rounded decimals.
• S241 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S240 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product72 with exact rational arithmetic, not rounded decimals.
• S239 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S238 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product71 with exact rational arithmetic, not rounded decimals.
• S237 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S236 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product70 with exact rational arithmetic, not rounded decimals.
• S235 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S234 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product69 with exact rational arithmetic, not rounded decimals.
• S233 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S232 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product68 with exact rational arithmetic, not rounded decimals.
• S231 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S230 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product67 with exact rational arithmetic, not rounded decimals.
• S229 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S228 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product66 with exact rational arithmetic, not rounded decimals.
• S227 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S226 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product65 with exact rational arithmetic, not rounded decimals.
• S225 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S224 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product64 with exact rational arithmetic, not rounded decimals.
• S223 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S222 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product63 with exact rational arithmetic, not rounded decimals.
• S221 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S220 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product62 with exact rational arithmetic, not rounded decimals.
• S219 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S218 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product61 with exact rational arithmetic, not rounded decimals.
• S217 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S216 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product60 with exact rational arithmetic, not rounded decimals.
• S215 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S214 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product59 with exact rational arithmetic, not rounded decimals.
• S213 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S212 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product58 with exact rational arithmetic, not rounded decimals.
• S211 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S210 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product57 with exact rational arithmetic, not rounded decimals.
• S209 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S208 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product56 with exact rational arithmetic, not rounded decimals.
• S207 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S206 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product55 with exact rational arithmetic, not rounded decimals.
• S205 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S204 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product54 with exact rational arithmetic, not rounded decimals.
• S203 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S202 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product53 with exact rational arithmetic, not rounded decimals.
• S201 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S200 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product52 with exact rational arithmetic, not rounded decimals.
• S199 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S198 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product51 with exact rational arithmetic, not rounded decimals.
• S197 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S196 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product50 with exact rational arithmetic, not rounded decimals.
• S195 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S194 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product49 with exact rational arithmetic, not rounded decimals.
• S193 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S192 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product48 with exact rational arithmetic, not rounded decimals.
• S191 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S190 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product47 with exact rational arithmetic, not rounded decimals.
• S189 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S188 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product46 with exact rational arithmetic, not rounded decimals.
• S187 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S186 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product45 with exact rational arithmetic, not rounded decimals.
• S185 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S184 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product44 with exact rational arithmetic, not rounded decimals.
• S183 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S182 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product43 with exact rational arithmetic, not rounded decimals.
• S181 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S180 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product42 with exact rational arithmetic, not rounded decimals.
• S179 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S178 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product41 with exact rational arithmetic, not rounded decimals.
• S177 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S176 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product40 with exact rational arithmetic, not rounded decimals.
• S175 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S174 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product39 with exact rational arithmetic, not rounded decimals.
• S173 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S172 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product38 with exact rational arithmetic, not rounded decimals.
• S171 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S170 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product37 with exact rational arithmetic, not rounded decimals.
• S169 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S168 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product36 with exact rational arithmetic, not rounded decimals.
• S167 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S166 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product35 with exact rational arithmetic, not rounded decimals.
• S165 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S164 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product34 with exact rational arithmetic, not rounded decimals.
• S163 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S162 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product33 with exact rational arithmetic, not rounded decimals.
• S161 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S160 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product32 with exact rational arithmetic, not rounded decimals.
• S159 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S158 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product31 with exact rational arithmetic, not rounded decimals.
• S157 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S156 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product30 with exact rational arithmetic, not rounded decimals.
• S155 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S154 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product29 with exact rational arithmetic, not rounded decimals.
• S153 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S152 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product28 with exact rational arithmetic, not rounded decimals.
• S151 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S150 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product27 with exact rational arithmetic, not rounded decimals.
• S149 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S148 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product26 with exact rational arithmetic, not rounded decimals.
• S147 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S146 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product25 with exact rational arithmetic, not rounded decimals.
• S145 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S144 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product24 with exact rational arithmetic, not rounded decimals.
• S143 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S142 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product23 with exact rational arithmetic, not rounded decimals.
• S141 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S140 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product22 with exact rational arithmetic, not rounded decimals.
• S139 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S138 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product21 with exact rational arithmetic, not rounded decimals.
• S137 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S136 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product20 with exact rational arithmetic, not rounded decimals.
• S135 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S134 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product19 with exact rational arithmetic, not rounded decimals.
• S133 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S132 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product18 with exact rational arithmetic, not rounded decimals.
• S131 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S130 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product17 with exact rational arithmetic, not rounded decimals.
• S129 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S128 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product16 with exact rational arithmetic, not rounded decimals.
• S127 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S126 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product15 with exact rational arithmetic, not rounded decimals.
• S125 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S124 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product14 with exact rational arithmetic, not rounded decimals.
• S123 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S122 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product13 with exact rational arithmetic, not rounded decimals.
• S121 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S120 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product12 with exact rational arithmetic, not rounded decimals.
• S119 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S118 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product11 with exact rational arithmetic, not rounded decimals.
• S117 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S116 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product10 with exact rational arithmetic, not rounded decimals.
• S115 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S114 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product9 with exact rational arithmetic, not rounded decimals.
• S113 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S112 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product8 with exact rational arithmetic, not rounded decimals.
• S111 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S110 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product7 with exact rational arithmetic, not rounded decimals.
• S109 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S108 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product6 with exact rational arithmetic, not rounded decimals.
• S107 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S106 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product5 with exact rational arithmetic, not rounded decimals.
• S105 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S104 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product4 with exact rational arithmetic, not rounded decimals.
• S103 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S102 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product3 with exact rational arithmetic, not rounded decimals.
• S101 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S100 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product2 with exact rational arithmetic, not rounded decimals.
• S099 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S098 · premise_and_result_audit — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product1 with exact rational arithmetic, not rounded decimals.
• S097 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S096 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S095 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S094 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S093 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S092 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S091 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S090 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S089 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S088 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S087 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S086 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S085 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S084 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S083 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S082 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S081 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S080 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S079 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S078 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S077 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S076 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S075 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S074 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S073 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S072 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S071 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S070 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S069 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S068 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S067 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S066 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S065 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S064 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S063 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S062 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S061 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S060 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S059 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S058 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S057 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S056 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S055 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S054 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S053 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S052 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S051 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S050 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S049 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S048 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S047 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S046 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S045 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S044 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S043 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S042 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S041 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S040 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S039 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S038 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S037 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S036 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S035 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S034 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S033 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S032 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S031 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S030 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S029 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S028 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S027 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S026 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S025 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S024 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S023 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S022 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S021 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S020 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S019 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S018 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S017 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S016 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S015 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S014 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S013 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S012 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S011 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S010 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S009 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S008 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S007 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S006 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S005 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S004 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S003 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S002 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S001 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.

Result

(97, [[1, 1], [2, 49], [3, 65], [4, 73], [5, 39], [6, 81], [7, 14], [8, 85], [9, 54], [10, 68], [11, 53], [12, 89], [13, 15], [14, 7], [15, 13], [16, 91], [17, 40], [18, 27], [19, 46], [20, 34], [21, 37], [22, 75], [23, 38], [24, 93], [25, 66], [26, 56], [27, 18], [28, 52], [29, 87], [30, 55], [31, 72], [32, 94], [33, 50], [34, 20], [35, 61], [36, 62], [37, 21], [38, 23], [39, 5], [40, 17], [41, 71], [42, 67], [43, 88], [44, 86], [45, 69], [46, 19], [47, 64], [48, 95], [49, 2], [50, 33], [51, 78], [52, 28], [53, 11], [54, 9], [55, 30], [56, 26], [57, 80], [58, 92], [59, 74], [60, 76], [61, 35], [62, 36], [63, 77], [64, 47], [65, 3], [66, 25], [67, 42], [68, 10], [69, 45], [70, 79], [71, 41], [72, 31], [73, 4], [74, 59], [75, 22], [76, 60], [77, 63], [78, 51], [79, 70], [80, 57], [81, 6], [82, 84], [83, 90], [84, 82], [85, 8], [86, 44], [87, 29], [88, 43], [89, 12], [90, 83], [91, 16], [92, 58], [93, 24], [94, 32], [95, 48], [96, 96]], [1, 96], [[2, 49, 1], [3, 65, 1], [4, 73, 1], [5, 39, 1], [6, 81, 1], [7, 14, 1], [8, 85, 1], [9, 54, 1], [10, 68, 1], [11, 53, 1], [12, 89, 1], [13, 15, 1], [16, 91, 1], [17, 40, 1], [18, 27, 1], [19, 46, 1], [20, 34, 1], [21, 37, 1], [22, 75, 1], [23, 38, 1], [24, 93, 1], [25, 66, 1], [26, 56, 1], [28, 52, 1], [29, 87, 1], [30, 55, 1], [31, 72, 1], [32, 94, 1], [33, 50, 1], [35, 61, 1], [36, 62, 1], [41, 71, 1], [42, 67, 1], [43, 88, 1], [44, 86, 1], [45, 69, 1], [47, 64, 1], [48, 95, 1], [51, 78, 1], [57, 80, 1], [58, 92, 1], [59, 74, 1], [60, 76, 1], [63, 77, 1], [70, 79, 1], [82, 84, 1], [83, 90, 1]], self_inverse_residues_1_and_p_minus_1, 96, Yes)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.