Jelaskan Wieferich primes dari Daftar bilangan prima

Primes p such that  for fixed integer a > 1.

2p − 1 ≡ 1 (mod p2): 1093, 3511 ()

3p − 1 ≡ 1 (mod p2): 11, 1006003 ()

4p − 1 ≡ 1 (mod p2): 1093, 3511

5p − 1 ≡ 1 (mod p2): 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 ()

6p − 1 ≡ 1 (mod p2): 66161, 534851, 3152573 ()

7p − 1 ≡ 1 (mod p2): 5, 491531 ()

8p − 1 ≡ 1 (mod p2): 3, 1093, 3511

9p − 1 ≡ 1 (mod p2): 2, 11, 1006003

10p − 1 ≡ 1 (mod p2): 3, 487, 56598313 ()

11p − 1 ≡ 1 (mod p2): 71

12p − 1 ≡ 1 (mod p2): 2693, 123653 ()

13p − 1 ≡ 1 (mod p2): 2, 863, 1747591 ()

14p − 1 ≡ 1 (mod p2): 29, 353, 7596952219 ()

15p − 1 ≡ 1 (mod p2): 29131, 119327070011 ()

16p − 1 ≡ 1 (mod p2): 1093, 3511

17p − 1 ≡ 1 (mod p2): 2, 3, 46021, 48947 ()

18p − 1 ≡ 1 (mod p2): 5, 7, 37, 331, 33923, 1284043 ()

19p − 1 ≡ 1 (mod p2): 3, 7, 13, 43, 137, 63061489 ()

20p − 1 ≡ 1 (mod p2): 281, 46457, 9377747, 122959073 ()

21p − 1 ≡ 1 (mod p2): 2

22p − 1 ≡ 1 (mod p2): 13, 673, 1595813, 492366587, 9809862296159 ()

23p − 1 ≡ 1 (mod p2): 13, 2481757, 13703077, 15546404183, 2549536629329 ()

24p − 1 ≡ 1 (mod p2): 5, 25633

25p − 1 ≡ 1 (mod p2): 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801

, these are all known Wieferich primes with a ≤ 25.

Primes p for which p divides (p−1)! + 1.

, these are the only known Wilson primes.

Primes p for which the binomial coefficient

, these are the only known Wolstenholme primes.

Of the form n×2 − 1.

7, 23, 383, 32212254719, 2833419889721787128217599, 195845982777569926302400511, 4776913109852041418248056622882488319 ()