Et al,
Earlier this month, someone posted a question regarding the
Mersenne number 5014947 and asked for its factors. Here is what I've
been able to gleam.
Sincerely yours,
Robert G. Wilson v
5014947 = 3*7*47*5081
and its divisors are 1, 3, 7, 21, 47, 141, 329, 987, 5081, 15243,
35567, 106701, 238807, 716421, 1671649 & 5014947.
f(n) = 2^f +1.
f(1) = 3.
f(3) = (1) * 3.
f(7) = (1) * 43.
f(21) = (1, 3, 7) * 5419.
f(47) = (1) * 283 * 165768537521.
f(141) = (1, 3, 47) * 1681003 * 35273039401 * 111349165273.
f(329) = (1, 7 ,47) * 659 * 762394321774681 *
359687424377961714750891763743933975334959200103759485840227631801.
f(987) = (1, 3, 7, 21, 47, 141, 329) * 5135123689810129 * C151.
f(5081) = (1) * 10163 * 243889 * Composite.
f(15243) = (1, 3, 5081) * 3048601 * Composite.
f(35567) = (1, 7, 5081) * Composite.
f(106701) = (1, 3, 7, 21, 5081, 15243, 35567) * Composite.
f(238807) = (1, 47, 5081) * Composite.
f(716421) = (1, 3, 47, 141, 5081, 15243, 238807) * Composite.
f(1671649) = (1, 7, 47, 329, 5081, 35567, 238807 ) * Composite.
M(5014947) = 2^5014947 -1 = (factors from f(n))
(1) 3,
(3) 3,
(7) 43,
(47) 283,
(329) 659,
(21) 5419,
(5081) 10163,
(5081) 243889,
(141) 1681003,
(15243) 3048601,
(106701) 14724739,
(5081) 2478643907,
(141) 35273039401,
(141) 111349165273,
(47) 165768537521,
(329) 762394321774681,
(987) 5135123689810129,
(329)
359687424377961714750891763743933975334959200103759485840227631801,
(987)
2169938845890939210595986882453006136908227137290342138096226473293044748893969050207434882048911068413643936897791965117470283570473755493061296806419,
time one very large composite which has at least 16 factors. Good
luck in finding them.
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