

A124121


Primes q which are the lesser of a double Wieferich prime pair. (List of known values of q in increasing order, without multiplicity.)


12




OFFSET

1,1


COMMENTS

Double Wieferich prime pairs are pairs of primes (p, q) such that q^(p1) == 1 (mod p^2) and p^(q1) == 1 (mod q^2). This sequence gives the primes q which are the lesser member (listed second) of such pairs, in increasing order, but without multiplicity:
For example, currently there are two known double Wieferich prime pairs (p, q) with q = 5: (1645333507, 5) and (188748146801, 5). In this sequence, 5 is only listed once, as a(3), and only the lesser value p=1645333507 is listed as A124122(3).
This is just the list of known pairs: there may be gaps, i.e. missing primes.


LINKS

Table of n, a(n) for n=1..6.
Yuri F. Bilu, Catalan's Conjecture, Seminaire Bourbaki, (20022003).
Michael Mossinghoff, Wieferich Prime Pairs, Barker Sequences, and Circulant Hadamard Matrices, as of Feb 12 2009.
Eric Weisstein's World of Mathematics, Double Wieferich Prime Pair
Wikipedia, Wieferich pair


PROG

(PARI) /* The following (highly unoptimized) code misses the value q=5 (corresponding to a very large value of p) */
default(primelimit, 1010000); forprime(q=1, default(primelimit), forprime(p=q+1, default(primelimit), Mod(p, q^2)^(q1)1 & next; Mod(q, p^2)^(p1)1  print1( q", ")  break)) \\ M. F. Hasler, Oct 08 2011


CROSSREFS

See A124122 for values of p.
Cf. A196511, A196733.
Sequence in context: A041131 A084960 A087543 * A208226 A259378 A155011
Adjacent sequences: A124118 A124119 A124120 * A124122 A124123 A124124


KEYWORD

nonn,hard,more


AUTHOR

N. J. A. Sloane, following an email from Robert G. Wilson v, Nov 30 2006


STATUS

approved



