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A108164 Semiprimes p*q where both p and q are primes of the form 6n+1 (A002476).

%I A108164 #28 May 20 2021 19:22:35
%S A108164 49,91,133,169,217,247,259,301,361,403,427,469,481,511,553,559,589,
%T A108164 679,703,721,763,793,817,871,889,949,961,973,1027,1057,1099,1141,1147,
%U A108164 1159,1261,1267,1273,1333,1339,1351,1369,1387,1393,1417,1477,1501,1561,1591
%N A108164 Semiprimes p*q where both p and q are primes of the form 6n+1 (A002476).
%C A108164 These are the products of terms from A107890 excluding multiples of 3.
%C A108164 Every semiprime not divisible by 2 or 3 must be in one of these three disjoint sets:
%C A108164 A108164 = the product of two primes of the form 6n+1 (A002476),
%C A108164 A108166 = the product of two primes of the form 6n-1 (A007528),
%C A108164 A108172 = the product of a prime of the form 6n+1 and a prime of the form 6n-1.
%C A108164 The product of two primes of the form 6n+1 is a semiprime of the form 6n+1.
%D A108164 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
%H A108164 Robert Israel, <a href="/A108164/b108164.txt">Table of n, a(n) for n = 1..10000</a>
%H A108164 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A108164 K. G. Reuschle, <a href="https://gdz.sub.uni-goettingen.de/id/PPN576716448?tify={%22pages%22:[9]}">Tafeln complexer Primzahlen</a>, Königl. Akademie der Wissenschaften, Berlin, 1875, p. 1.
%F A108164 {a(n)} = {p*q where both p and q are in A002476}.
%p A108164 N:= 2000: # To get all terms <= N
%p A108164 P:= select(isprime, [seq(i,i=7..N/7, 6)]):
%p A108164 sort(select(`<=`,[seq(seq(P[i]*P[j],j=1..i),i=1..nops(P))],N)); # _Robert Israel_, Dec 27 2018
%t A108164 With[{nn=50},Take[Times@@@Tuples[Select[6*Range[nn]+1,PrimeQ],2]// Union,nn]] (* _Harvey P. Dale_, May 20 2021 *)
%Y A108164 Cf. A001358, A002476, A107890.
%K A108164 easy,nonn
%O A108164 1,1
%A A108164 _Jonathan Vos Post_, Jun 13 2005
%E A108164 Edited and extended by _Ray Chandler_, Oct 15 2005