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COMMENTS
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b known Wieferich primes in base b (multiplicative order of b mod these primes (also these primes^2)) (if the order is p-1, then b is a primitive root to mod this prime (but not mod this prime^2), see A055578)
2 1093 (364), 3511 (1755)
3 11 (5), 1006003 (1006002)
4 1093 (182), 3511 (1755)
5 2 (1), 20771 (10385), 40487 (40486), 53471161 (13367790), 1645333507 (1645333506), 6692367337 (6692367336), 188748146801 (11796759175)
6 66161 (66160), 534851 (106970), 3152573 (788143)
7 5 (4), 491531 (245765)
8 3 (2), 1093 (364), 3511 (585)
9 2 (1), 11 (5), 1006003 (503001)
10 3 (1), 487 (486), 56598313 (56598312)
11 71 (70)
12 2693 (2692), 123653 (123652)
13 2 (1), 863 (862), 1747591 (873795)
14 29 (28), 353 (352), 7596952219 (7596952218)
15 29131 (29130), 119327070011 (59663535005)
16 1093 (91), 3511 (1755)
17 2 (1), 3 (2), 46021 (7670), 48947 (24473), 478225523351 (478225523350)
18 5 (4), 7 (3), 37 (36), 331 (110), 33923 (33922), 1284043 (428014)
19 3 (1), 7 (6), 13 (12), 43 (42), 137 (68), 63061489 (63061488)
20 281 (140), 46457 (46456), 9377747 (9377746), 122959073 (122959072)
21 2 (1)
22 13 (3), 673 (224), 1595813 (797906), 492366587 (246183293), 9809862296159 (44999368331)
23 13 (6), 2481757 (827252), 13703077 (13703076), 15546404183 (7773202091), 2549536629329 (2549536629328)
24 5 (2), 25633 (6408)
These orders n will satisfy that Phi_n(b) is divisible by p^2, where Phi is the cyclotomic polynomial. (Usually, Phi_n(b) is squarefree, but these are all exceptions; i.e., if p^2 divides Phi_n(b) (except the case p = 2, n = 2 and b == 3 (mod 4)), then p is a Wieferich prime in base b.)
(End)
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