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A061576 Smallest prime of irregularity index n. 9
2, 3, 37, 157, 491, 12613, 78233, 527377, 3238481, 381348997, 1767218027 (list; graph; refs; listen; history; text; internal format)



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.


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.


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


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




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


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



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Last modified April 21 04:01 EDT 2021. Contains 343146 sequences. (Running on oeis4.)