A286208 Greater of Wilson's pseudo-twin primes: primes q such that p! == 1 (mod q), where p=A151799(q) is the previous prime before q, and q-p>2.

7853, 594278556271609021, 4259842839142238791410741595983041626644087509

Offset: 1

Author

Max Alekseyev and Thomas Ordowski, May 04 2017

Keywords

• bref
• nonn
• more

Comments

By Wilson's theorem, p! == 1 (mod p+2) whenever (p,p+2) are twin primes. This sequence and A286181 concern consecutive primes (p,q) satisfying p! = 1 (mod q), where d = q-p > 2.

It follows that (d-1)! == 1 (mod q). Listed terms correspond to d = 12, 30, 76 (cf. A286230). Further terms should have d>=140.

Also, primes q=prime(n) such that A275111(n-1)=1, and (prime(n-1),prime(n)) are not twin primes (i.e., q is not a term of A006512).

Crossrefs

Subsequence of A166864.

Cf. A275111, A286181, A286230.