A061576 Smallest prime of irregularity index n.

2, 3, 37, 157, 491, 12613, 78233, 527377, 3238481, 381348997, 1767218027

Offset

-1,1

Comments

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.

References

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

Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag, NY, 2004, page 226.

Links

Table of n, a(n) for n=-1..9.

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. P. Buhler, R. E. Crandall, R. Ernvall et al., Irregular primes and cyclotomic invariants to 12 Million, J. Symbolic Computation 31 (2001) 89-96.

W. Hart, D. Harvey and W. Ong, Irregular primes to two billion, Mathematics of Computation, 86 (2017), 3031-3049; also available at arXiv:1605.02398 [math.NT], 2016.

Math. Pages, On the Density of Some Exceptional Primes

Eric Weisstein's World of Mathematics, Irregular Prime.

Bernoulli numbers, irregularity index of primes

Crossrefs

Cf. A091887, A000928, A007703, A073276, A073277, A060975, A219332, A219333, A219334, A219335, A297848.

Sequence in context: A258455 A118370 A189027 * A221055 A144466 A245061

Adjacent sequences: A061573 A061574 A061575 * A061577 A061578 A061579

Keyword

nonn,nice,hard,more

Author

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

Extensions

a(8)-a(9) added by Amiram Eldar, Aug 23 2018 from the paper by Hart et al.

Status

approved