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A364186
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Primes p such that p divides 2^((p-1)/x) - 1, where x is the smallest odd prime factor of p - 1.
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0
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31, 43, 109, 127, 157, 223, 229, 251, 277, 283, 307, 397, 431, 433, 439, 457, 499, 601, 641, 643, 691, 727, 733, 739, 811, 911, 919, 953, 971, 997, 1013, 1021, 1051, 1069, 1093, 1103, 1163, 1181, 1327, 1399, 1423, 1459, 1471, 1579, 1597, 1627, 1657, 1699, 1709
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OFFSET
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1,1
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REFERENCES
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Allan Cunningham, Haupt-exponents of 2, The Quarterly Journal of Pure and Applied Mathematics, Vol. 37 (1906), pp. 122-145.
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LINKS
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PROG
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(Magma) [p: p in PrimesUpTo(1709) | #Factorization(p-1) ge 2 and Modexp(2, Truncate((p-1)/Factorization(p-1)[2][1]), p) eq 1];
(PARI) forprime(p=2, 1709, v=Vec(factor(p-1))[1]; if(#v>1, t=0; e=v[2]; x=floor(p^(1/e))+1; until(x==p||t==2, if(Mod(x, p)^e==2, t++); x++); if(t==2, print1(p, ", "))));
(PARI) isok(p) = my(v=Vec(factor(p-1))[1]); isprime(p) && #v>1 && Mod(2, p)^((p-1)/v[2])==1;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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