A196511 Primes q for which there are primes b < c < p such that b^p == c^p == 1 (mod q^2).

555383, 1767407, 2103107, 2452757, 7400567, 12836987, 14668163, 15404867, 16238303, 19572647, 22796069, 25003799, 26978663, 27370727

Offset: 1

Author

M. F. Hasler, Oct 03 2011

Keywords

• nonn
• more

Comments

Computed mainly by M. Oakes and D. Broadhurst, cf. link.

For all the listed terms, except for a(4)=2452757 and a(11)=22796069, p=(q-1)/2, which implies that they are "safe primes", cf. A005385. For a(4) and a(11), p=(q-1)/4.

The subsequence of terms of the form q=2p+1 is A196733. As of today it is complete up to its 51st term, ~2e8. - M. F. Hasler, Oct 05 2011

Links

• D. J. Broadhurst et al., Re: Square factors of b^p-1 on yahoo group "primenumbers", Sept.-Oct. 2011
• David Broadhurst and others, Square factors of b^p-1, digest of 81 messages in primenumbers Yahoo group, Sep 22 - Nov 29, 2011.

Crossrefs

Cf. A196733, A124121, A124122, A005384, A005385.