

A157352


Products (semiprimes) of two distinct safe primes.


9



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
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OFFSET

1,1


COMMENTS

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


LINKS



EXAMPLE

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.


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[(c1)/2]&&PrimeQ[(d1)/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 *)


CROSSREFS

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


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



