A272627 Numbers n = pq where p, q are primes congruent to 3 and 7 mod 8, respectively.

21, 69, 77, 93, 133, 141, 213, 237, 253, 301, 309, 341, 381, 413, 437, 453, 469, 501, 517, 573, 581, 589, 597, 669, 717, 749, 781, 789, 813, 869, 893, 917, 933, 973, 989, 1077, 1101, 1133, 1141, 1149, 1253, 1293, 1317, 1333, 1349, 1357, 1389, 1397, 1437, 1461

Offset: 1

Author

Morgan L. Owens, May 03 2016

Keywords

• nonn

Comments

Candidate moduli for Rabin cryptosystem using Williams padding to ensure sufficient redundancy that the decryption is unique.

References

• Steven D. Galbraith, Mathematics of Public Key Cryptography, Cambridge University Press, 2012, page 493.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• H. C. Williams, A Modification of the RSA public encryption procedure, IEEE Trans. Inf. Theory 26(6) (1980), 726-729.

Crossrefs

Cf. A016105.

Programs

Mathematica

With[{upto = 1000},
With[{primes = Prime@Range@PrimePi@NextPrime[upto/3]},
  With[{p = Pick[primes, Mod[primes, 8], 3], q = Pick[primes, Mod[primes, 8], 7]},
   Select[Union[Flatten@Outer[Times, p, q]], # <= upto &]] ]] (* after Harvey P. Dale at A016105 *)

PARI

ok(n)={n%8==5 && bigomega(n)==2 && factor(n)[1,1] % 4 == 3} \\ Andrew Howroyd, Dec 23 2019

Extensions

Terms a(36) and beyond from Andrew Howroyd, Dec 23 2019