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A016047
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Smallest prime factor of Mersenne numbers.
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15
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3, 7, 31, 127, 23, 8191, 131071, 524287, 47, 233, 2147483647, 223, 13367, 431, 2351, 6361, 179951, 2305843009213693951, 193707721, 228479, 439, 2687, 167, 618970019642690137449562111, 11447, 7432339208719, 2550183799, 162259276829213363391578010288127
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listen;
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OFFSET
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1,1
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COMMENTS
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Submitted new b-file withdrawing last three terms previously submitted. I had, before submitting that b-file, checked that the smallest known factors of incompletely factored Mersenne numbers was less than the known trial factoring limits recorded by Will Edgington in his LowM.txt file which can be found on his Mersenne page, (see link above.) I have now discovered that I inadvertently omitted the purported a(203) from that check. - Daran Gill, Apr 05 2013
The would-be a(203) corresponds to 2^1237-1 which is currently P70*C303. Trial factoring has only been done to 60 bits, and since its difficulty doubles whenever the bit length is incremented by one, it cannot exhaustively search the space smaller than the sole known 70-digit (231-bit) factor. Probabilistic ECM testing indicates only that it is extremely unlikely that there is any undiscovered factor with digit-size smaller than the high fifties. See GIMPS links. - Gord Palameta, Aug 16 2018
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LINKS
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MATHEMATICA
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a = {}; Do[If[PrimeQ[n], w = 2^n - 1; c = FactorInteger[w]; b = c[[1]][[1]]; AppendTo[a, b]], {n, 2, 100}]; a (* Artur Jasinski, Dec 11 2007 *)
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PROG
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(PARI) forprime(p=2, 150, print1(factor(2^p-1)[1, 1], ", "))
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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STATUS
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approved
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