第 27796 題：Wilson定理

原題與已知條件

n>1、factorial congruence與prime-residue inverse pairing責任。操作=wilson-prime-inverse-pairing；資料={"p":73}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — n>1、factorial congruence與prime-residue inverse pairing責任。操作=wilson-prime-inverse-pairing；資料={"p":73}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-wilson-theorem

逐步推導

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 = [73, 1]

derived = [1, 1]

source roles = [73, 2]

derived = [37, 1]

source roles = [73, 3]

derived = [49, 1]

source roles = [73, 4]

derived = [55, 1]

source roles = [73, 5]

derived = [44, 1]

source roles = [73, 6]

derived = [61, 1]

source roles = [73, 7]

derived = [21, 1]

source roles = [73, 8]

derived = [64, 1]

source roles = [73, 9]

derived = [65, 1]

source roles = [73, 10]

derived = [22, 1]

source roles = [73, 11]

derived = [20, 1]

source roles = [73, 12]

derived = [67, 1]

source roles = [73, 13]

derived = [45, 1]

source roles = [73, 14]

derived = [47, 1]

source roles = [73, 15]

derived = [39, 1]

source roles = [73, 16]

derived = [32, 1]

source roles = [73, 17]

derived = [43, 1]

source roles = [73, 18]

derived = [69, 1]

source roles = [73, 19]

derived = [50, 1]

source roles = [73, 20]

derived = [11, 1]

source roles = [73, 21]

derived = [7, 1]

source roles = [73, 22]

derived = [10, 1]

source roles = [73, 23]

derived = [54, 1]

source roles = [73, 24]

derived = [70, 1]

source roles = [73, 25]

derived = [38, 1]

source roles = [73, 26]

derived = [59, 1]

source roles = [73, 27]

derived = [46, 1]

source roles = [73, 28]

derived = [60, 1]

source roles = [73, 29]

derived = [68, 1]

source roles = [73, 30]

derived = [56, 1]

source roles = [73, 31]

derived = [33, 1]

source roles = [73, 32]

derived = [16, 1]

source roles = [73, 33]

derived = [31, 1]

source roles = [73, 34]

derived = [58, 1]

source roles = [73, 35]

derived = [48, 1]

source roles = [73, 36]

derived = [71, 1]

source roles = [73, 37]

derived = [2, 1]

source roles = [73, 38]

derived = [25, 1]

source roles = [73, 39]

derived = [15, 1]

source roles = [73, 40]

derived = [42, 1]

source roles = [73, 41]

derived = [57, 1]

source roles = [73, 42]

derived = [40, 1]

source roles = [73, 43]

derived = [17, 1]

source roles = [73, 44]

derived = [5, 1]

source roles = [73, 45]

derived = [13, 1]

source roles = [73, 46]

derived = [27, 1]

source roles = [73, 47]

derived = [14, 1]

source roles = [73, 48]

derived = [35, 1]

source roles = [73, 49]

derived = [3, 1]

source roles = [73, 50]

derived = [19, 1]

source roles = [73, 51]

derived = [63, 1]

source roles = [73, 52]

derived = [66, 1]

source roles = [73, 53]

derived = [62, 1]

source roles = [73, 54]

derived = [23, 1]

source roles = [73, 55]

derived = [4, 1]

source roles = [73, 56]

derived = [30, 1]

source roles = [73, 57]

derived = [41, 1]

source roles = [73, 58]

derived = [34, 1]

source roles = [73, 59]

derived = [26, 1]

source roles = [73, 60]

derived = [28, 1]

source roles = [73, 61]

derived = [6, 1]

source roles = [73, 62]

derived = [53, 1]

source roles = [73, 63]

derived = [51, 1]

source roles = [73, 64]

derived = [8, 1]

source roles = [73, 65]

derived = [9, 1]

source roles = [73, 66]

derived = [52, 1]

source roles = [73, 67]

derived = [12, 1]

source roles = [73, 68]

derived = [29, 1]

source roles = [73, 69]

derived = [18, 1]

source roles = [73, 70]

derived = [24, 1]

source roles = [73, 71]

derived = [36, 1]

source roles = [73, 72]

derived = [72, 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, 73, 1, 1, 1]

derived = [0, 1, 是, 是]

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, 73, 2, 1, 2]

derived = [0, 2, 是, 是]

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, 73, 3, 2, 6]

derived = [0, 6, 是, 是]

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, 73, 4, 6, 24]

derived = [0, 24, 是, 是]

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, 73, 5, 24, 120]

derived = [1, 47, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product6 := mul(47, 6)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product6 = 282

source roles = [Wilson ORIGINAL prime factorial, 73, 6, 47, 282]

derived = [3, 63, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product7 := mul(63, 7)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product7 = 441

source roles = [Wilson ORIGINAL prime factorial, 73, 7, 63, 441]

derived = [6, 3, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product8 := mul(3, 8)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product8 = 24

source roles = [Wilson ORIGINAL prime factorial, 73, 8, 3, 24]

derived = [0, 24, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product9 := mul(24, 9)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product9 = 216

source roles = [Wilson ORIGINAL prime factorial, 73, 9, 24, 216]

derived = [2, 70, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product10 := mul(70, 10)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product10 = 700

source roles = [Wilson ORIGINAL prime factorial, 73, 10, 70, 700]

derived = [9, 43, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product11 := mul(43, 11)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product11 = 473

source roles = [Wilson ORIGINAL prime factorial, 73, 11, 43, 473]

derived = [6, 35, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product12 := mul(35, 12)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product12 = 420

source roles = [Wilson ORIGINAL prime factorial, 73, 12, 35, 420]

derived = [5, 55, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product13 := mul(55, 13)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product13 = 715

source roles = [Wilson ORIGINAL prime factorial, 73, 13, 55, 715]

derived = [9, 58, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product14 := mul(58, 14)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product14 = 812

source roles = [Wilson ORIGINAL prime factorial, 73, 14, 58, 812]

derived = [11, 9, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product15 := mul(9, 15)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product15 = 135

source roles = [Wilson ORIGINAL prime factorial, 73, 15, 9, 135]

derived = [1, 62, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product16 := mul(62, 16)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product16 = 992

source roles = [Wilson ORIGINAL prime factorial, 73, 16, 62, 992]

derived = [13, 43, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product17 := mul(43, 17)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product17 = 731

source roles = [Wilson ORIGINAL prime factorial, 73, 17, 43, 731]

derived = [10, 1, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product18 := mul(1, 18)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product18 = 18

source roles = [Wilson ORIGINAL prime factorial, 73, 18, 1, 18]

derived = [0, 18, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product19 := mul(18, 19)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product19 = 342

source roles = [Wilson ORIGINAL prime factorial, 73, 19, 18, 342]

derived = [4, 50, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product20 := mul(50, 20)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product20 = 1000

source roles = [Wilson ORIGINAL prime factorial, 73, 20, 50, 1000]

derived = [13, 51, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product21 := mul(51, 21)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product21 = 1071

source roles = [Wilson ORIGINAL prime factorial, 73, 21, 51, 1071]

derived = [14, 49, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product22 := mul(49, 22)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product22 = 1078

source roles = [Wilson ORIGINAL prime factorial, 73, 22, 49, 1078]

derived = [14, 56, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product23 := mul(56, 23)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product23 = 1288

source roles = [Wilson ORIGINAL prime factorial, 73, 23, 56, 1288]

derived = [17, 47, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product24 := mul(47, 24)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product24 = 1128

source roles = [Wilson ORIGINAL prime factorial, 73, 24, 47, 1128]

derived = [15, 33, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product25 := mul(33, 25)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product25 = 825

source roles = [Wilson ORIGINAL prime factorial, 73, 25, 33, 825]

derived = [11, 22, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product26 := mul(22, 26)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product26 = 572

source roles = [Wilson ORIGINAL prime factorial, 73, 26, 22, 572]

derived = [7, 61, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product27 := mul(61, 27)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product27 = 1647

source roles = [Wilson ORIGINAL prime factorial, 73, 27, 61, 1647]

derived = [22, 41, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product28 := mul(41, 28)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product28 = 1148

source roles = [Wilson ORIGINAL prime factorial, 73, 28, 41, 1148]

derived = [15, 53, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product29 := mul(53, 29)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product29 = 1537

source roles = [Wilson ORIGINAL prime factorial, 73, 29, 53, 1537]

derived = [21, 4, 是, 是]

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, 73, 30, 4, 120]

derived = [1, 47, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product31 := mul(47, 31)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product31 = 1457

source roles = [Wilson ORIGINAL prime factorial, 73, 31, 47, 1457]

derived = [19, 70, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product32 := mul(70, 32)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product32 = 2240

source roles = [Wilson ORIGINAL prime factorial, 73, 32, 70, 2240]

derived = [30, 50, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product33 := mul(50, 33)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product33 = 1650

source roles = [Wilson ORIGINAL prime factorial, 73, 33, 50, 1650]

derived = [22, 44, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product34 := mul(44, 34)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product34 = 1496

source roles = [Wilson ORIGINAL prime factorial, 73, 34, 44, 1496]

derived = [20, 36, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product35 := mul(36, 35)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product35 = 1260

source roles = [Wilson ORIGINAL prime factorial, 73, 35, 36, 1260]

derived = [17, 19, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product36 := mul(19, 36)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product36 = 684

source roles = [Wilson ORIGINAL prime factorial, 73, 36, 19, 684]

derived = [9, 27, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product37 := mul(27, 37)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product37 = 999

source roles = [Wilson ORIGINAL prime factorial, 73, 37, 27, 999]

derived = [13, 50, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product38 := mul(50, 38)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product38 = 1900

source roles = [Wilson ORIGINAL prime factorial, 73, 38, 50, 1900]

derived = [26, 2, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product39 := mul(2, 39)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product39 = 78

source roles = [Wilson ORIGINAL prime factorial, 73, 39, 2, 78]

derived = [1, 5, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product40 := mul(5, 40)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product40 = 200

source roles = [Wilson ORIGINAL prime factorial, 73, 40, 5, 200]

derived = [2, 54, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product41 := mul(54, 41)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product41 = 2214

source roles = [Wilson ORIGINAL prime factorial, 73, 41, 54, 2214]

derived = [30, 24, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product42 := mul(24, 42)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product42 = 1008

source roles = [Wilson ORIGINAL prime factorial, 73, 42, 24, 1008]

derived = [13, 59, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product43 := mul(59, 43)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product43 = 2537

source roles = [Wilson ORIGINAL prime factorial, 73, 43, 59, 2537]

derived = [34, 55, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product44 := mul(55, 44)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product44 = 2420

source roles = [Wilson ORIGINAL prime factorial, 73, 44, 55, 2420]

derived = [33, 11, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product45 := mul(11, 45)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product45 = 495

source roles = [Wilson ORIGINAL prime factorial, 73, 45, 11, 495]

derived = [6, 57, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product46 := mul(57, 46)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product46 = 2622

source roles = [Wilson ORIGINAL prime factorial, 73, 46, 57, 2622]

derived = [35, 67, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product47 := mul(67, 47)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product47 = 3149

source roles = [Wilson ORIGINAL prime factorial, 73, 47, 67, 3149]

derived = [43, 10, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product48 := mul(10, 48)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product48 = 480

source roles = [Wilson ORIGINAL prime factorial, 73, 48, 10, 480]

derived = [6, 42, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product49 := mul(42, 49)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product49 = 2058

source roles = [Wilson ORIGINAL prime factorial, 73, 49, 42, 2058]

derived = [28, 14, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product50 := mul(14, 50)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product50 = 700

source roles = [Wilson ORIGINAL prime factorial, 73, 50, 14, 700]

derived = [9, 43, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product51 := mul(43, 51)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product51 = 2193

source roles = [Wilson ORIGINAL prime factorial, 73, 51, 43, 2193]

derived = [30, 3, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product52 := mul(3, 52)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product52 = 156

source roles = [Wilson ORIGINAL prime factorial, 73, 52, 3, 156]

derived = [2, 10, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product53 := mul(10, 53)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product53 = 530

source roles = [Wilson ORIGINAL prime factorial, 73, 53, 10, 530]

derived = [7, 19, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product54 := mul(19, 54)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product54 = 1026

source roles = [Wilson ORIGINAL prime factorial, 73, 54, 19, 1026]

derived = [14, 4, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product55 := mul(4, 55)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product55 = 220

source roles = [Wilson ORIGINAL prime factorial, 73, 55, 4, 220]

derived = [3, 1, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product56 := mul(1, 56)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product56 = 56

source roles = [Wilson ORIGINAL prime factorial, 73, 56, 1, 56]

derived = [0, 56, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product57 := mul(56, 57)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product57 = 3192

source roles = [Wilson ORIGINAL prime factorial, 73, 57, 56, 3192]

derived = [43, 53, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product58 := mul(53, 58)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product58 = 3074

source roles = [Wilson ORIGINAL prime factorial, 73, 58, 53, 3074]

derived = [42, 8, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product59 := mul(8, 59)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product59 = 472

source roles = [Wilson ORIGINAL prime factorial, 73, 59, 8, 472]

derived = [6, 34, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product60 := mul(34, 60)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product60 = 2040

source roles = [Wilson ORIGINAL prime factorial, 73, 60, 34, 2040]

derived = [27, 69, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product61 := mul(69, 61)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product61 = 4209

source roles = [Wilson ORIGINAL prime factorial, 73, 61, 69, 4209]

derived = [57, 48, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product62 := mul(48, 62)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product62 = 2976

source roles = [Wilson ORIGINAL prime factorial, 73, 62, 48, 2976]

derived = [40, 56, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product63 := mul(56, 63)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product63 = 3528

source roles = [Wilson ORIGINAL prime factorial, 73, 63, 56, 3528]

derived = [48, 24, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product64 := mul(24, 64)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product64 = 1536

source roles = [Wilson ORIGINAL prime factorial, 73, 64, 24, 1536]

derived = [21, 3, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product65 := mul(3, 65)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product65 = 195

source roles = [Wilson ORIGINAL prime factorial, 73, 65, 3, 195]

derived = [2, 49, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product66 := mul(49, 66)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product66 = 3234

source roles = [Wilson ORIGINAL prime factorial, 73, 66, 49, 3234]

derived = [44, 22, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product67 := mul(22, 67)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product67 = 1474

source roles = [Wilson ORIGINAL prime factorial, 73, 67, 22, 1474]

derived = [20, 14, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product68 := mul(14, 68)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product68 = 952

source roles = [Wilson ORIGINAL prime factorial, 73, 68, 14, 952]

derived = [13, 3, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product69 := mul(3, 69)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product69 = 207

source roles = [Wilson ORIGINAL prime factorial, 73, 69, 3, 207]

derived = [2, 61, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product70 := mul(61, 70)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product70 = 4270

source roles = [Wilson ORIGINAL prime factorial, 73, 70, 61, 4270]

derived = [58, 36, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product71 := mul(36, 71)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product71 = 2556

source roles = [Wilson ORIGINAL prime factorial, 73, 71, 36, 2556]

derived = [35, 1, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product72 := mul(1, 72)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product72 = 72

source roles = [Wilson ORIGINAL prime factorial, 73, 72, 1, 72]

derived = [0, 72, 是, 是]

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

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

逐步反向核對

• S218 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S217 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S216 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product72，不以小數近似替代。
• S215 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S214 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product71，不以小數近似替代。
• S213 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S212 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product70，不以小數近似替代。
• S211 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S210 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product69，不以小數近似替代。
• S209 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S208 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product68，不以小數近似替代。
• S207 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S206 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product67，不以小數近似替代。
• S205 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S204 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product66，不以小數近似替代。
• S203 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S202 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product65，不以小數近似替代。
• S201 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S200 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product64，不以小數近似替代。
• S199 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S198 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product63，不以小數近似替代。
• S197 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S196 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product62，不以小數近似替代。
• S195 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S194 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product61，不以小數近似替代。
• S193 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S192 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product60，不以小數近似替代。
• S191 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S190 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product59，不以小數近似替代。
• S189 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S188 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product58，不以小數近似替代。
• S187 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S186 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product57，不以小數近似替代。
• S185 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S184 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product56，不以小數近似替代。
• S183 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S182 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product55，不以小數近似替代。
• S181 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S180 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product54，不以小數近似替代。
• S179 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S178 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product53，不以小數近似替代。
• S177 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S176 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product52，不以小數近似替代。
• S175 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S174 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product51，不以小數近似替代。
• S173 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S172 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product50，不以小數近似替代。
• S171 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S170 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product49，不以小數近似替代。
• S169 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S168 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product48，不以小數近似替代。
• S167 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S166 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product47，不以小數近似替代。
• S165 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S164 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product46，不以小數近似替代。
• S163 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S162 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product45，不以小數近似替代。
• S161 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S160 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product44，不以小數近似替代。
• S159 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S158 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product43，不以小數近似替代。
• S157 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S156 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product42，不以小數近似替代。
• S155 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S154 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product41，不以小數近似替代。
• S153 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S152 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product40，不以小數近似替代。
• S151 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S150 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product39，不以小數近似替代。
• S149 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S148 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product38，不以小數近似替代。
• S147 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S146 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product37，不以小數近似替代。
• S145 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S144 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product36，不以小數近似替代。
• S143 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S142 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product35，不以小數近似替代。
• S141 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S140 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product34，不以小數近似替代。
• S139 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S138 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product33，不以小數近似替代。
• S137 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S136 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product32，不以小數近似替代。
• S135 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S134 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product31，不以小數近似替代。
• S133 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S132 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product30，不以小數近似替代。
• S131 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S130 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product29，不以小數近似替代。
• S129 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S128 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product28，不以小數近似替代。
• S127 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S126 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product27，不以小數近似替代。
• S125 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S124 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product26，不以小數近似替代。
• S123 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S122 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product25，不以小數近似替代。
• S121 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S120 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product24，不以小數近似替代。
• S119 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S118 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product23，不以小數近似替代。
• S117 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S116 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product22，不以小數近似替代。
• S115 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S114 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product21，不以小數近似替代。
• S113 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S112 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product20，不以小數近似替代。
• S111 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S110 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product19，不以小數近似替代。
• S109 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S108 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product18，不以小數近似替代。
• S107 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S106 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product17，不以小數近似替代。
• S105 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S104 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product16，不以小數近似替代。
• S103 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S102 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product15，不以小數近似替代。
• S101 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S100 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product14，不以小數近似替代。
• S099 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S098 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product13，不以小數近似替代。
• S097 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S096 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product12，不以小數近似替代。
• S095 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S094 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product11，不以小數近似替代。
• S093 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S092 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product10，不以小數近似替代。
• S091 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S090 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product9，不以小數近似替代。
• S089 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S088 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product8，不以小數近似替代。
• S087 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S086 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product7，不以小數近似替代。
• S085 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S084 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product6，不以小數近似替代。
• S083 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S082 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product5，不以小數近似替代。
• S081 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S080 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product4，不以小數近似替代。
• S079 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S078 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product3，不以小數近似替代。
• S077 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S076 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product2，不以小數近似替代。
• S075 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S074 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product1，不以小數近似替代。
• S073 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S072 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S071 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S070 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S069 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S068 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S067 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S066 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S065 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S064 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S063 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S062 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S061 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S060 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S059 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S058 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S057 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S056 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S055 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S054 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S053 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S052 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S051 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S050 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S049 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S048 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S047 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S046 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S045 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S044 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S043 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S042 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S041 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S040 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S039 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S038 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S037 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S036 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S035 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S034 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S033 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S032 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S031 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S030 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S029 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S028 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S027 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S026 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S025 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S024 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S023 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S022 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S021 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S020 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S019 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S018 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S017 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S016 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S015 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S014 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S013 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S012 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S011 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S010 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S009 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S008 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S007 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S006 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S005 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S004 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S003 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S002 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S001 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。

結論

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

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。