-1,1

By convention 2 has irregularity index -1; regular primes (the first is 3, see A007703) have index 0; an irregular prime of index n >= 1 is an irregular prime p (see A000928) such that p divides exactly n Bernoulli numbers B_{2i} with 2i < p-1.

J. Buhler, R. Crandall, R. Ernvall and T. Metsankyla, Irregular primes and cyclotomic invariants to four million. Math. Comp. 61 (1993), no. 203, 151-153.

J. Buhler, R. Crandall, R. Ernvall, T. Metsankyla and M. A. Shokrollahi, Irregular Primes and Cyclotomic Invariants to 12 Million, J. Symbolic Computation 31, 2001, 89-96.

P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, NY, 1995, page 326.

Math. Pages, On the Density of Some Exceptional Primes

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Bernoulli numbers, irregularity index of primes

Cf. A007703, A000928.

Sequence in context: A109748 A062459 A118370 this_sequence A144466 A041329 A060813

Adjacent sequences: A061573 A061574 A061575 this_sequence A061577 A061578 A061579

nonn,nice,hard

William G. McCallum (wmc(AT)math.arizona.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), May 20 2001