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

1,1

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.

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 *)

Prog

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

Crossrefs

Cf. A016105.

Sequence in context: A180758 A197121 A175461 * A043339 A023712 A045124

Adjacent sequences: A272624 A272625 A272626 * A272628 A272629 A272630

Keyword

nonn

Author

Morgan L. Owens, May 03 2016

Extensions

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

Status

approved