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A258074 Table read by rows: each row represents the constant and exponent of a Colbert number.

%I A258074 #52 Oct 07 2023 21:38:41
%S A258074 5359,5054502,33661,7031232,28433,7830457,27653,9167433,19249,
%T A258074 13018586,10223,31172165
%N A258074 Table read by rows: each row represents the constant and exponent of a Colbert number.
%C A258074 Each row has two entries [k,n]. With this notation, the corresponding Colbert number is k*2^n+1.
%C A258074 A Colbert number is an integer with more than 1,000,000 digits that is prime and has contributed to the in-progress computational proof that 78557 is the smallest Sierpiński number (A076336).
%C A258074 a(11)-a(12) number, corresponding to [10223,31172165], is the second largest known prime that is not a Mersenne prime as of August 2023. - _Hermann Stamm-Wilbrandt_, Aug 13 2023
%C A258074 This table can only have (and is expected to have) five more rows corresponding to constants k equal to 21181, 22699, 24737, 55459, and 67607.
%H A258074 C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/ColbertNumber.html">Colbert Number</a>
%H A258074 C. K. Caldwell, The Prime Database, <a href="https://primes.utm.edu/primes/page.php?id=122473">10223*2^31172165+1</a>
%H A258074 W. Sierpiński, <a href="http://dx.doi.org/10.5169/seals-20713">Sur un problème concernant les nombres k * 2^n + 1</a>, Elem. Math., 15 (1960), pp. 73-74.
%H A258074 Hermann Stamm-Wilbrandt, <a href="https://github.com/Hermann-SW/Colbert_numbers">Colbert numbers</a>, contains entries [k,n,s,x,y] for the 6 Colbert numbers, with p=k*2^n+1, s^2%p==p-1 and p==x^2+y^2.
%H A258074 Wikipedia, <a href="http://en.wikipedia.org/wiki/Seventeen_or_Bust">Seventeen or Bust</a>
%e A258074 The table is as follows:
%e A258074   5359, 5054502;
%e A258074   33661, 7031232;
%e A258074   28433, 7830457;
%e A258074   27653, 9167433;
%e A258074   19249, 13018586
%e A258074   10223, 31172165
%Y A258074 Cf. A076336, A064699, A064721.
%K A258074 nonn,tabf,fini,more
%O A258074 1,1
%A A258074 _Tom Edgar_, May 18 2015
%E A258074 a(11)-a(12) from _Richard N. Smith_, Jul 15 2019, following by the prime 10223*2^31172165+1 found by PrimeGrid.