A108166 Semiprimes p*q where both p and q are primes of the form 6n-1 (A007528).

25, 55, 85, 115, 121, 145, 187, 205, 235, 253, 265, 289, 295, 319, 355, 391, 415, 445, 451, 493, 505, 517, 529, 535, 565, 583, 649, 655, 667, 685, 697, 745, 781, 799, 835, 841, 865, 895, 901, 913, 943, 955, 979, 985, 1003, 1081, 1111, 1135, 1165, 1177, 1189

Offset: 1

Author

Jonathan Vos Post, Jun 13 2005

Keywords

• easy
• nonn

Comments

Every semiprime not divisible by 2 or 3 must be in one of these three disjoint sets:

A108164 - the product of two primes of the form 6n + 1 (A002476),

A108166 - the product of two primes of the form 6n - 1 (A007528),

A108172 - the product of a prime of the form 6n + 1 and a prime of the form 6n - 1.

The product of two primes of the form 6n - 1 is a semiprime of the form 6n + 1.

References

• Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A001358, A007528.

Programs

Mathematica

Module[{nn = 150, pf}, pf = Select[6Range[nn] - 1, PrimeQ]; Take[Union[Times@@@Tuples[pf, 2]], nn/2]] (* Harvey P. Dale, Dec 09 2013 *)
Select[6Range[200] + 1, PrimeOmega[#] == 2 && Mod[FactorInteger[#][[1, 1]], 6] == 5 &] (* Alonso del Arte, Aug 24 2017 *)

Formula

{a(n)} = {p*q where both p and q are in A007528}.

Extensions

Edited and extended by Ray Chandler, Oct 15 2005