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%I #15 Dec 23 2019 18:57:12
%S 21,69,77,93,133,141,213,237,253,301,309,341,381,413,437,453,469,501,
%T 517,573,581,589,597,669,717,749,781,789,813,869,893,917,933,973,989,
%U 1077,1101,1133,1141,1149,1253,1293,1317,1333,1349,1357,1389,1397,1437,1461
%N Numbers n = pq where p, q are primes congruent to 3 and 7 mod 8, respectively.
%C Candidate moduli for Rabin cryptosystem using Williams padding to ensure sufficient redundancy that the decryption is unique.
%D Steven D. Galbraith, Mathematics of Public Key Cryptography, Cambridge University Press, 2012, page 493.
%H Andrew Howroyd, <a href="/A272627/b272627.txt">Table of n, a(n) for n = 1..1000</a>
%H H. C. Williams, <a href="http://dx.doi.org/10.1109/TIT.1980.1056264">A Modification of the RSA public encryption procedure</a>, IEEE Trans. Inf. Theory 26(6) (1980), 726-729.
%t With[{upto = 1000},
%t With[{primes = Prime@Range@PrimePi@NextPrime[upto/3]},
%t With[{p = Pick[primes, Mod[primes, 8], 3], q = Pick[primes, Mod[primes, 8], 7]},
%t Select[Union[Flatten@Outer[Times, p, q]], # <= upto &]] ]] (* after _Harvey P. Dale_ at A016105 *)
%o (PARI) ok(n)={n%8==5 && bigomega(n)==2 && factor(n)[1,1] % 4 == 3} \\ _Andrew Howroyd_, Dec 23 2019
%Y Cf. A016105.
%K nonn
%O 1,1
%A _Morgan L. Owens_, May 03 2016
%E Terms a(36) and beyond from _Andrew Howroyd_, Dec 23 2019
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