Prime q=2*p+1 with primes b<c<p such that q^2|b^p-1 and q^2|c^p-1

555383, 1767407, 2103107, 7400567, 12836987, 14668163, 15404867,

16238303, 19572647, 25003799, 26978663, 27370727, 35182919,

36180527, 38553023, 39714083, 52503587, 53061143, 53735699,

55072427, 63302159, 70728839, 77199743, 77401679, 86334299,

97298759, 97375319, 103830599, 106208783, 106710287, 108711599,

112590683, 120441239, 124581719, 126236879, 128538659, 129881603,

133833983, 141132143, 141194387, 145553399, 151565087

Comments: (p,q) is a Sophie Germain prime pair; (b,q) and (c,q)

are Wieferich prime pairs; each of (b,c) is a square modulo q^2.

The sequence is now complete up to the 42nd term, q=151565087.

Mike Oakes set a puzzle on a more general case with primes such

that b<p1<q, c<p2<q, b<c, q^2|b^p1-1 and q^2|c^p2-1. His sequence

is complete only up q=27370727, containing only two new known

primes, q=2452757 and q=22796069, with p1=p2=(q-1)/4, found in

http://tech.groups.yahoo.com/group/primenumbers/message/23175 by

a simple analysis of

http://www.cecm.sfu.ca/~mjm/WieferichBarker
David Broadhurst, 4 October 2011, with thanks to Mike Oakes