A157352 Products (semiprimes) of two distinct safe primes.

35, 55, 77, 115, 161, 235, 253, 295, 329, 413, 415, 517, 535, 581, 649, 749, 835, 895, 913, 1081, 1135, 1169, 1177, 1253, 1315, 1357, 1589, 1735, 1795, 1837, 1841, 1909, 1915, 1969, 2335, 2395, 2429, 2461, 2497, 2513, 2515, 2681, 2773, 2815, 2893, 2935

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

• nonn

Comments

35=5*7; 5 and 7 are safe primes, 55=5*11; 5 and 11 are safe primes,...

Examples

			a(1) = 35 since 35 = 5 * 7, and (5 - 1)/2 = 2 and (7 - 1)/2 = 3 are both prime, thus 5 and 7 are distinct safe primes.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A005384, A005385, A006881, A007304, A111206, A157342, A157344, A157345, A157346, A157347.

Programs

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[(c-1)/2]&&PrimeQ[(d-1)/2],AppendTo[lst,n]]]],{n,7!}];lst
Select[Select[Range@ 3000, PrimeNu@ # == 2 &], Times @@ Map[If[PrimeQ[(# - 1)/2], #, 0] &, Map[First, FactorInteger@ #]] == # &] (* Michael De Vlieger, Feb 28 2016 *)
Module[{upto=3000,sp},sp=Select[Prime[Range[PrimePi[upto/5]]],PrimeQ[(#-1)/2]&];Select[Union[Times@@@Subsets[sp,{2}]],#<+upto&]] (* Harvey P. Dale, Aug 25 2017 *)

Extensions

Example corrected by Harvey P. Dale, Aug 25 2017