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A162730 Semiprimes n = pq such that q = kp - k + 1, where p,q primes and k > 1. 2

%I #15 Sep 18 2018 05:25:08

%S 6,10,14,15,21,22,26,33,34,38,39,46,51,57,58,62,65,69,74,82,85,86,87,

%T 91,93,94,106,111,118,122,123,129,133,134,141,142,145,146,158,159,166,

%U 177,178,183,185,194,201,202,205,206,213,214,217,218,219,226,237,249,254

%N Semiprimes n = pq such that q = kp - k + 1, where p,q primes and k > 1.

%C It seems that most of the semiprimes of this form (but not all, only those satisfying an additional property) can be factored very quickly (e.g. numbers with up to 1200 decimal digits can be factored in a couple of seconds) using a very simple method.

%C Squarefree semiprimes n such that lpf(n)-1 divides n-1. Semiprimes n = pq with primes p < q such that p-1 divides q-1. If n is such a semiprime, then q^n == q (mod n). - _Thomas Ordowski_, Sep 18 2018

%o (PARI) isok(n) = {if ((bigomega(n) == 2) && (omega(n) == 2), my(p = factor(n)[1, 1], q = factor(n)[2, 1]); (q-1) % (p-1) == 0;);} \\ _Michel Marcus_, Sep 18 2018

%Y Subsequence of A006881 (squarefree semiprimes).

%K nonn

%O 1,1

%A _Vassilis Papadimitriou_, Jul 12 2009, Jul 13 2009

%E More terms from _R. J. Mathar_, Aug 06 2009

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