A060975 Irregular primes with irregularity index three.
491, 617, 647, 1151, 1217, 1811, 1847, 2939, 3833, 4003, 4657, 4951, 6763, 7687, 8831, 9011, 10463, 10589, 12073, 13217, 14533, 14737, 14957, 15287, 15787, 15823, 16007, 17681, 17863, 18713, 18869, 20533, 20939, 24019, 24659, 25153, 26561
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated by Hart et al., terms 1..9824 from T. D. Noe, calculated by Buhler et al.)
- 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.
- Bernoulli numbers, irregularity index of primes
- William Hart, David Harvey and Wilson Ong, Irregular primes to two billion, Mathematics of Computation, Vol. 86, No. 308 (2017), pp. 3031-3049; also available at arXiv:1605.02398 [math.NT], 2016.
- David Harvey, Irregular primes to two billion (includes a list of all primes less than 2^31).
Programs
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Mathematica
Do[p = Prime[n]; k = 1; c = 0; While[ 2*k < p - 3, If[ Mod[ Numerator[ BernoulliB[2*k]], p] == 0, c++ ]; k++ ]; If[ c == 3, Print[p]], {n, 3, 1000} ] Do[p = Prime@n; k = 1; c = 0; While[ 2*k < p - 3, If[ Mod[ Numerator[ BernoulliB[2*k]], p] == 0, c++ ]; k++ ]; If[ c == 3, Print@p], {n, 3, 13887} ]
Extensions
Extended by Robert G. Wilson v, Sep 20 2006