login
A157344
Semiprimes that are the product of two distinct Sophie Germain primes.
11
6, 10, 15, 22, 33, 46, 55, 58, 69, 82, 87, 106, 115, 123, 145, 159, 166, 178, 205, 226, 249, 253, 262, 265, 267, 319, 339, 346, 358, 382, 393, 415, 445, 451, 466, 478, 502, 519, 537, 562, 565, 573, 583, 586, 655, 667, 699, 717, 718, 753, 838, 843, 862, 865
OFFSET
1,1
COMMENTS
6=2*3; 2 and 3 are Sophie Germain primes, 10=2*5; 2 and 5 are Sophie Germain primes, 15=3*5; 3 and 5 are Sophie Germain primes, ...
LINKS
MATHEMATICA
lst={}; Do[If[Plus@@Last/@FactorInteger[n]==2, a=Length[First/@FactorInteger[n]]; If[a==2, b=First/@FactorInteger[n]; c=b[[1]]; d=b[[2]]; If[PrimeQ[2*c+1]&&PrimeQ[2*d+1], AppendTo[lst, n]]]], {n, 7!}]; lst
nn=100; With[{sgp=Select[Prime[Range[nn]], PrimeQ[2#+1]&]}, Take[ Union[ Select[ Times @@@ Subsets[sgp, {2}], PrimeOmega[#]==2&]], nn]] (* Harvey P. Dale, Nov 22 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved