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 A007703 Regular primes. (Formerly M2411) 12
 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 269, 277, 281, 313, 317, 331, 337, 349, 359, 367, 373, 383, 397, 419, 431 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A prime p is regular if and only if the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) are not divisible by p. REFERENCES Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 425-430. H. M. Edwards, Fermat's Last Theorem, Springer, 1977. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 C. K. Caldwell, The Prime Glossary, Regular prime K. Conrad, Fermat's Last Theorem For Regular Primes F. Luca, A. Pizarro-Madariaga, C. Pomerance, On the counting function of irregular primes, 2014. O. A. Ivanova, Regular prime number D. Jao, PlanetMath.org, Regular prime A. L. Robledo, PlanetMath.org, examples of regular primes Eric Weisstein's World of Mathematics, Regular Prime MATHEMATICA s = {}; Do[p = Prime@n; k = 1; While[2k <= p - 3 && Mod[Numerator@BernoulliB[2k], p] != 0, k++ ]; If[2k > p - 3, AppendTo[s, p]], {n, 2, 80}]; s (* Robert G. Wilson v Sep 20 2006 *) PROG (PARI) is(p)=forstep(k=2, p-3, 2, if(numerator(bernfrac(k))%p==0, return(0))); isprime(p) \\ Charles R Greathouse IV, Feb 25 2014 (Python) from sympy import prime, isprime, bernoulli def ok(n):     for k in range(2, n - 2, 2):         if bernoulli(k).as_numer_denom()[0] % n == 0:             return 0     return isprime(n) [n for n in range(3, 501) if ok(n)] # Indranil Ghosh, Jun 27 2017, after Charles R Greathouse IV CROSSREFS Cf. A000928 (irregular primes) and A061576 for further references. Sequence in context: A165255 A223036 A155058 * A002556 A130101 A130057 Adjacent sequences:  A007700 A007701 A007702 * A007704 A007705 A007706 KEYWORD nonn,nice AUTHOR EXTENSIONS Corrected by Gerard Schildberger, Jun 01 2004 STATUS approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)