OFFSET
1,1
COMMENTS
"Mersenne numbers", here, implies A001348. Compare to sequence A049479, where "Mersenne numbers" is used in the sense of A000225. - Lekraj Beedassy, Jun 11 2009
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
LINKS
Daran Gill, Table of n, a(n) for n = 1..202 (first 95 terms from T. D. Noe)
C. K. Caldwell, Mersenne Primes
Will Edgington, Mersenne Page
GIMPS, PrimeNet Known Factors of Mersenne Numbers (discovered recently for p < 2000), Exponent status of 2^1237 - 1, ECM testing status of 2^1237 - 1
Brady Haran and Matt Parker, How they found the World's Biggest Prime Number - Numberphile, Numberphile video (2016).
FORMULA
MAPLE
a:= n-> min(numtheory[factorset](2^ithprime(n)-1)):
seq(a(n), n=1..28); # Alois P. Heinz, Oct 01 2024
MATHEMATICA
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 *)
PROG
(PARI) forprime(p=2, 150, print1(factor(2^p-1)[1, 1], ", "))
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
STATUS
approved