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%I #7 Aug 19 2022 09:13:46
%S 3277,29341,49141,80581,88357,104653,196093,314821,458989,476971,
%T 489997,800605,838861,873181,877099,1004653,1251949,1302451,1325843,
%U 1373653,1397419,1441091,1507963,1509709,1530787,1678541,1811573,1907851,1987021,2004403,2269093
%N Odd composite numbers k such that 2^((k-1)/2) == -1 (mod k).
%C Counterexamples (pseudoprimes) to the hypothesis that this congruence is sufficient to prove that an odd number is prime.
%C Compare with Proth's theorem.
%t Select[Range[1, 2.5*10^6, 2], CompositeQ[#] && PowerMod[2, (# - 1)/2, #] == # - 1 &] (* _Amiram Eldar_, Aug 19 2022 *)
%o (PARI) forstep(k=3,10^8,2,isprime(k)&&next();Mod(2,k)^((k-1)/2)==-1&&print1(k,", "))
%Y Cf. A244626, A244628.
%K nonn
%O 1,1
%A _Jeppe Stig Nielsen_, Aug 19 2022