Question 27799: All Nonzero Prime Residues Pair with Inverses, with a Special p=2 Case

Original question and givens

Use prime modulus p=89. Give (p, all_inverse_pairs, self_inverse_residues, distinct_cancelling_pairs, self_inverse_scope, factorial_residue, Wilson_congruence).

• G001 — Use prime modulus p=89. 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 = [89, 1]

derived = [1, 1]

source roles = [89, 2]

derived = [45, 1]

source roles = [89, 3]

derived = [30, 1]

source roles = [89, 4]

derived = [67, 1]

source roles = [89, 5]

derived = [18, 1]

source roles = [89, 6]

derived = [15, 1]

source roles = [89, 7]

derived = [51, 1]

source roles = [89, 8]

derived = [78, 1]

source roles = [89, 9]

derived = [10, 1]

source roles = [89, 10]

derived = [9, 1]

source roles = [89, 11]

derived = [81, 1]

source roles = [89, 12]

derived = [52, 1]

source roles = [89, 13]

derived = [48, 1]

source roles = [89, 14]

derived = [70, 1]

source roles = [89, 15]

derived = [6, 1]

source roles = [89, 16]

derived = [39, 1]

source roles = [89, 17]

derived = [21, 1]

source roles = [89, 18]

derived = [5, 1]

source roles = [89, 19]

derived = [75, 1]

source roles = [89, 20]

derived = [49, 1]

source roles = [89, 21]

derived = [17, 1]

source roles = [89, 22]

derived = [85, 1]

source roles = [89, 23]

derived = [31, 1]

source roles = [89, 24]

derived = [26, 1]

source roles = [89, 25]

derived = [57, 1]

source roles = [89, 26]

derived = [24, 1]

source roles = [89, 27]

derived = [33, 1]

source roles = [89, 28]

derived = [35, 1]

source roles = [89, 29]

derived = [43, 1]

source roles = [89, 30]

derived = [3, 1]

source roles = [89, 31]

derived = [23, 1]

source roles = [89, 32]

derived = [64, 1]

source roles = [89, 33]

derived = [27, 1]

source roles = [89, 34]

derived = [55, 1]

source roles = [89, 35]

derived = [28, 1]

source roles = [89, 36]

derived = [47, 1]

source roles = [89, 37]

derived = [77, 1]

source roles = [89, 38]

derived = [82, 1]

source roles = [89, 39]

derived = [16, 1]

source roles = [89, 40]

derived = [69, 1]

source roles = [89, 41]

derived = [76, 1]

source roles = [89, 42]

derived = [53, 1]

source roles = [89, 43]

derived = [29, 1]

source roles = [89, 44]

derived = [87, 1]

source roles = [89, 45]

derived = [2, 1]

source roles = [89, 46]

derived = [60, 1]

source roles = [89, 47]

derived = [36, 1]

source roles = [89, 48]

derived = [13, 1]

source roles = [89, 49]

derived = [20, 1]

source roles = [89, 50]

derived = [73, 1]

source roles = [89, 51]

derived = [7, 1]

source roles = [89, 52]

derived = [12, 1]

source roles = [89, 53]

derived = [42, 1]

source roles = [89, 54]

derived = [61, 1]

source roles = [89, 55]

derived = [34, 1]

source roles = [89, 56]

derived = [62, 1]

source roles = [89, 57]

derived = [25, 1]

source roles = [89, 58]

derived = [66, 1]

source roles = [89, 59]

derived = [86, 1]

source roles = [89, 60]

derived = [46, 1]

source roles = [89, 61]

derived = [54, 1]

source roles = [89, 62]

derived = [56, 1]

source roles = [89, 63]

derived = [65, 1]

source roles = [89, 64]

derived = [32, 1]

source roles = [89, 65]

derived = [63, 1]

source roles = [89, 66]

derived = [58, 1]

source roles = [89, 67]

derived = [4, 1]

source roles = [89, 68]

derived = [72, 1]

source roles = [89, 69]

derived = [40, 1]

source roles = [89, 70]

derived = [14, 1]

source roles = [89, 71]

derived = [84, 1]

source roles = [89, 72]

derived = [68, 1]

source roles = [89, 73]

derived = [50, 1]

source roles = [89, 74]

derived = [83, 1]

source roles = [89, 75]

derived = [19, 1]

source roles = [89, 76]

derived = [41, 1]

source roles = [89, 77]

derived = [37, 1]

source roles = [89, 78]

derived = [8, 1]

source roles = [89, 79]

derived = [80, 1]

source roles = [89, 80]

derived = [79, 1]

source roles = [89, 81]

derived = [11, 1]

source roles = [89, 82]

derived = [38, 1]

source roles = [89, 83]

derived = [74, 1]

source roles = [89, 84]

derived = [71, 1]

source roles = [89, 85]

derived = [22, 1]

source roles = [89, 86]

derived = [59, 1]

source roles = [89, 87]

derived = [44, 1]

source roles = [89, 88]

derived = [88, 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, 89, 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, 89, 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, 89, 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, 89, 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, 89, 5, 24, 120]

derived = [1, 31, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product6 := mul(31, 6)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product6 = 186

source roles = [Wilson ORIGINAL prime factorial, 89, 6, 31, 186]

derived = [2, 8, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product7 := mul(8, 7)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product7 = 56

source roles = [Wilson ORIGINAL prime factorial, 89, 7, 8, 56]

derived = [0, 56, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product8 := mul(56, 8)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product8 = 448

source roles = [Wilson ORIGINAL prime factorial, 89, 8, 56, 448]

derived = [5, 3, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product9 := mul(3, 9)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product9 = 27

source roles = [Wilson ORIGINAL prime factorial, 89, 9, 3, 27]

derived = [0, 27, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product10 := mul(27, 10)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product10 = 270

source roles = [Wilson ORIGINAL prime factorial, 89, 10, 27, 270]

derived = [3, 3, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product11 := mul(3, 11)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product11 = 33

source roles = [Wilson ORIGINAL prime factorial, 89, 11, 3, 33]

derived = [0, 33, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product12 := mul(33, 12)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product12 = 396

source roles = [Wilson ORIGINAL prime factorial, 89, 12, 33, 396]

derived = [4, 40, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product13 := mul(40, 13)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product13 = 520

source roles = [Wilson ORIGINAL prime factorial, 89, 13, 40, 520]

derived = [5, 75, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product14 := mul(75, 14)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product14 = 1050

source roles = [Wilson ORIGINAL prime factorial, 89, 14, 75, 1050]

derived = [11, 71, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product15 := mul(71, 15)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product15 = 1065

source roles = [Wilson ORIGINAL prime factorial, 89, 15, 71, 1065]

derived = [11, 86, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product16 := mul(86, 16)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product16 = 1376

source roles = [Wilson ORIGINAL prime factorial, 89, 16, 86, 1376]

derived = [15, 41, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product17 := mul(41, 17)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product17 = 697

source roles = [Wilson ORIGINAL prime factorial, 89, 17, 41, 697]

derived = [7, 74, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product18 := mul(74, 18)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product18 = 1332

source roles = [Wilson ORIGINAL prime factorial, 89, 18, 74, 1332]

derived = [14, 86, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product19 := mul(86, 19)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product19 = 1634

source roles = [Wilson ORIGINAL prime factorial, 89, 19, 86, 1634]

derived = [18, 32, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product20 := mul(32, 20)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product20 = 640

source roles = [Wilson ORIGINAL prime factorial, 89, 20, 32, 640]

derived = [7, 17, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product21 := mul(17, 21)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product21 = 357

source roles = [Wilson ORIGINAL prime factorial, 89, 21, 17, 357]

derived = [4, 1, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product22 := mul(1, 22)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product22 = 22

source roles = [Wilson ORIGINAL prime factorial, 89, 22, 1, 22]

derived = [0, 22, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product23 := mul(22, 23)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product23 = 506

source roles = [Wilson ORIGINAL prime factorial, 89, 23, 22, 506]

derived = [5, 61, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product24 := mul(61, 24)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product24 = 1464

source roles = [Wilson ORIGINAL prime factorial, 89, 24, 61, 1464]

derived = [16, 40, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product25 := mul(40, 25)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product25 = 1000

source roles = [Wilson ORIGINAL prime factorial, 89, 25, 40, 1000]

derived = [11, 21, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product26 := mul(21, 26)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product26 = 546

source roles = [Wilson ORIGINAL prime factorial, 89, 26, 21, 546]

derived = [6, 12, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product27 := mul(12, 27)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product27 = 324

source roles = [Wilson ORIGINAL prime factorial, 89, 27, 12, 324]

derived = [3, 57, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product28 := mul(57, 28)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product28 = 1596

source roles = [Wilson ORIGINAL prime factorial, 89, 28, 57, 1596]

derived = [17, 83, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product29 := mul(83, 29)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product29 = 2407

source roles = [Wilson ORIGINAL prime factorial, 89, 29, 83, 2407]

derived = [27, 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, 89, 30, 4, 120]

derived = [1, 31, Yes, Yes]

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

Wilson ORIGINAL prime factorial ORIGINAL running factorial product31 = 961

source roles = [Wilson ORIGINAL prime factorial, 89, 31, 31, 961]

derived = [10, 71, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product32 := mul(71, 32)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product32 = 2272

source roles = [Wilson ORIGINAL prime factorial, 89, 32, 71, 2272]

derived = [25, 47, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product33 := mul(47, 33)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product33 = 1551

source roles = [Wilson ORIGINAL prime factorial, 89, 33, 47, 1551]

derived = [17, 38, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product34 := mul(38, 34)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product34 = 1292

source roles = [Wilson ORIGINAL prime factorial, 89, 34, 38, 1292]

derived = [14, 46, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product35 := mul(46, 35)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product35 = 1610

source roles = [Wilson ORIGINAL prime factorial, 89, 35, 46, 1610]

derived = [18, 8, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product36 := mul(8, 36)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product36 = 288

source roles = [Wilson ORIGINAL prime factorial, 89, 36, 8, 288]

derived = [3, 21, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product37 := mul(21, 37)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product37 = 777

source roles = [Wilson ORIGINAL prime factorial, 89, 37, 21, 777]

derived = [8, 65, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product38 := mul(65, 38)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product38 = 2470

source roles = [Wilson ORIGINAL prime factorial, 89, 38, 65, 2470]

derived = [27, 67, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product39 := mul(67, 39)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product39 = 2613

source roles = [Wilson ORIGINAL prime factorial, 89, 39, 67, 2613]

derived = [29, 32, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product40 := mul(32, 40)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product40 = 1280

source roles = [Wilson ORIGINAL prime factorial, 89, 40, 32, 1280]

derived = [14, 34, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product41 := mul(34, 41)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product41 = 1394

source roles = [Wilson ORIGINAL prime factorial, 89, 41, 34, 1394]

derived = [15, 59, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product42 := mul(59, 42)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product42 = 2478

source roles = [Wilson ORIGINAL prime factorial, 89, 42, 59, 2478]

derived = [27, 75, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product43 := mul(75, 43)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product43 = 3225

source roles = [Wilson ORIGINAL prime factorial, 89, 43, 75, 3225]

derived = [36, 21, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product44 := mul(21, 44)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product44 = 924

source roles = [Wilson ORIGINAL prime factorial, 89, 44, 21, 924]

derived = [10, 34, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product45 := mul(34, 45)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product45 = 1530

source roles = [Wilson ORIGINAL prime factorial, 89, 45, 34, 1530]

derived = [17, 17, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product46 := mul(17, 46)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product46 = 782

source roles = [Wilson ORIGINAL prime factorial, 89, 46, 17, 782]

derived = [8, 70, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product47 := mul(70, 47)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product47 = 3290

source roles = [Wilson ORIGINAL prime factorial, 89, 47, 70, 3290]

derived = [36, 86, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product48 := mul(86, 48)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product48 = 4128

source roles = [Wilson ORIGINAL prime factorial, 89, 48, 86, 4128]

derived = [46, 34, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product49 := mul(34, 49)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product49 = 1666

source roles = [Wilson ORIGINAL prime factorial, 89, 49, 34, 1666]

derived = [18, 64, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product50 := mul(64, 50)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product50 = 3200

source roles = [Wilson ORIGINAL prime factorial, 89, 50, 64, 3200]

derived = [35, 85, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product51 := mul(85, 51)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product51 = 4335

source roles = [Wilson ORIGINAL prime factorial, 89, 51, 85, 4335]

derived = [48, 63, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product52 := mul(63, 52)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product52 = 3276

source roles = [Wilson ORIGINAL prime factorial, 89, 52, 63, 3276]

derived = [36, 72, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product53 := mul(72, 53)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product53 = 3816

source roles = [Wilson ORIGINAL prime factorial, 89, 53, 72, 3816]

derived = [42, 78, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product54 := mul(78, 54)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product54 = 4212

source roles = [Wilson ORIGINAL prime factorial, 89, 54, 78, 4212]

derived = [47, 29, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product55 := mul(29, 55)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product55 = 1595

source roles = [Wilson ORIGINAL prime factorial, 89, 55, 29, 1595]

derived = [17, 82, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product56 := mul(82, 56)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product56 = 4592

source roles = [Wilson ORIGINAL prime factorial, 89, 56, 82, 4592]

derived = [51, 53, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product57 := mul(53, 57)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product57 = 3021

source roles = [Wilson ORIGINAL prime factorial, 89, 57, 53, 3021]

derived = [33, 84, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product58 := mul(84, 58)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product58 = 4872

source roles = [Wilson ORIGINAL prime factorial, 89, 58, 84, 4872]

derived = [54, 66, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product59 := mul(66, 59)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product59 = 3894

source roles = [Wilson ORIGINAL prime factorial, 89, 59, 66, 3894]

derived = [43, 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, 89, 60, 67, 4020]

derived = [45, 15, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product61 := mul(15, 61)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product61 = 915

source roles = [Wilson ORIGINAL prime factorial, 89, 61, 15, 915]

derived = [10, 25, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product62 := mul(25, 62)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product62 = 1550

source roles = [Wilson ORIGINAL prime factorial, 89, 62, 25, 1550]

derived = [17, 37, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product63 := mul(37, 63)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product63 = 2331

source roles = [Wilson ORIGINAL prime factorial, 89, 63, 37, 2331]

derived = [26, 17, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product64 := mul(17, 64)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product64 = 1088

source roles = [Wilson ORIGINAL prime factorial, 89, 64, 17, 1088]

derived = [12, 20, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product65 := mul(20, 65)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product65 = 1300

source roles = [Wilson ORIGINAL prime factorial, 89, 65, 20, 1300]

derived = [14, 54, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product66 := mul(54, 66)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product66 = 3564

source roles = [Wilson ORIGINAL prime factorial, 89, 66, 54, 3564]

derived = [40, 4, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product67 := mul(4, 67)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product67 = 268

source roles = [Wilson ORIGINAL prime factorial, 89, 67, 4, 268]

derived = [3, 1, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product68 := mul(1, 68)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product68 = 68

source roles = [Wilson ORIGINAL prime factorial, 89, 68, 1, 68]

derived = [0, 68, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product69 := mul(68, 69)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product69 = 4692

source roles = [Wilson ORIGINAL prime factorial, 89, 69, 68, 4692]

derived = [52, 64, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product70 := mul(64, 70)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product70 = 4480

source roles = [Wilson ORIGINAL prime factorial, 89, 70, 64, 4480]

derived = [50, 30, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product71 := mul(30, 71)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product71 = 2130

source roles = [Wilson ORIGINAL prime factorial, 89, 71, 30, 2130]

derived = [23, 83, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product72 := mul(83, 72)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product72 = 5976

source roles = [Wilson ORIGINAL prime factorial, 89, 72, 83, 5976]

derived = [67, 13, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product73 := mul(13, 73)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product73 = 949

source roles = [Wilson ORIGINAL prime factorial, 89, 73, 13, 949]

derived = [10, 59, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product74 := mul(59, 74)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product74 = 4366

source roles = [Wilson ORIGINAL prime factorial, 89, 74, 59, 4366]

derived = [49, 5, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product75 := mul(5, 75)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product75 = 375

source roles = [Wilson ORIGINAL prime factorial, 89, 75, 5, 375]

derived = [4, 19, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product76 := mul(19, 76)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product76 = 1444

source roles = [Wilson ORIGINAL prime factorial, 89, 76, 19, 1444]

derived = [16, 20, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product77 := mul(20, 77)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product77 = 1540

source roles = [Wilson ORIGINAL prime factorial, 89, 77, 20, 1540]

derived = [17, 27, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product78 := mul(27, 78)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product78 = 2106

source roles = [Wilson ORIGINAL prime factorial, 89, 78, 27, 2106]

derived = [23, 59, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product79 := mul(59, 79)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product79 = 4661

source roles = [Wilson ORIGINAL prime factorial, 89, 79, 59, 4661]

derived = [52, 33, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product80 := mul(33, 80)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product80 = 2640

source roles = [Wilson ORIGINAL prime factorial, 89, 80, 33, 2640]

derived = [29, 59, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product81 := mul(59, 81)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product81 = 4779

source roles = [Wilson ORIGINAL prime factorial, 89, 81, 59, 4779]

derived = [53, 62, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product82 := mul(62, 82)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product82 = 5084

source roles = [Wilson ORIGINAL prime factorial, 89, 82, 62, 5084]

derived = [57, 11, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product83 := mul(11, 83)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product83 = 913

source roles = [Wilson ORIGINAL prime factorial, 89, 83, 11, 913]

derived = [10, 23, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product84 := mul(23, 84)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product84 = 1932

source roles = [Wilson ORIGINAL prime factorial, 89, 84, 23, 1932]

derived = [21, 63, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product85 := mul(63, 85)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product85 = 5355

source roles = [Wilson ORIGINAL prime factorial, 89, 85, 63, 5355]

derived = [60, 15, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product86 := mul(15, 86)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product86 = 1290

source roles = [Wilson ORIGINAL prime factorial, 89, 86, 15, 1290]

derived = [14, 44, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product87 := mul(44, 87)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product87 = 3828

source roles = [Wilson ORIGINAL prime factorial, 89, 87, 44, 3828]

derived = [43, 1, Yes, Yes]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product88 := mul(1, 88)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product88 = 88

source roles = [Wilson ORIGINAL prime factorial, 89, 88, 1, 88]

derived = [0, 88, Yes, Yes]

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

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

Reverse checks

• S266 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• 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 product88 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 product87 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 product86 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 product85 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 product84 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 product83 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 product82 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 product81 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 product80 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 product79 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 product78 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 product77 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 product76 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 product75 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 product74 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 product73 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 product72 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 product71 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 product70 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 product69 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 product68 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 product67 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 product66 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 product65 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 product64 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 product63 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 product62 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 product61 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 product60 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 product59 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 product58 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 product57 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 product56 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 product55 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 product54 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 product53 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 product52 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 product51 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 product50 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 product49 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 product48 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 product47 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 product46 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 product45 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 product44 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 product43 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 product42 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 product41 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 product40 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 product39 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 product38 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 product37 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 product36 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 product35 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 product34 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 product33 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 product32 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 product31 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 product30 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 product29 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 product28 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 product27 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 product26 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 product25 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 product24 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 product23 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 product22 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 product21 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 product20 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 product19 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 product18 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 product17 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 product16 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 product15 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 product14 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 product13 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 product12 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 product11 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 product10 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 product9 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 product8 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 product7 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 product6 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 product5 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 — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product4 with exact rational arithmetic, not rounded decimals.
• 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 — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product3 with exact rational arithmetic, not rounded decimals.
• 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 — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product2 with exact rational arithmetic, not rounded decimals.
• 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 — Recompute Wilson ORIGINAL prime factorial ORIGINAL running factorial product1 with exact rational arithmetic, not rounded decimals.
• 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

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