Small Mersenne Prime Factors (page 744/5610)

Small Mersenne Prime Factors
Prime numbers of the form M_p= 2^p − 1 are called Mersenne primes. For M_p to be prime, p must also be prime.
Any factor q of a Mersenne number 2^p − 1 must be of the form 2kp + 1, where integer k ≥ 0. Furthermore, q must be 1 or 7 mod 8.

Exp.	Prime Factor	Digits	Year
5514689	77205647	8	~1986
5514697	33088183	8	~1985
5514797	44118377	8	~1985
5514863	11029727	8	~1984
5515019	11030039	8	~1984
5515087	55150871	8	~1985
5515091	99271639	8	~1986
5515151	11030303	8	~1984
5515271	11030543	8	~1984
5515397	33092383	8	~1985
5515501	33093007	8	~1985
5515619	11031239	8	~1984
5516123	11032247	8	~1984
5516237	33097423	8	~1985
5516471	11032943	8	~1984
5516639	11033279	8	~1984
5516647	55166471	8	~1985
5516723	11033447	8	~1984
5516939	893744119	9	~1988
5517059	11034119	8	~1984
5517067	55170671	8	~1985
5517209	77240927	8	~1986
5517257	132414169	9	~1986
5517313	121380887	9	~1986
5517419	44139353	8	~1985

Exp.	Prime Factor	Digits	Year
5517599	44140793	8	~1985
5517667	353130689	9	~1987
5517727	55177271	8	~1985
5517839	11035679	8	~1984
5517893	33107359	8	~1985
5517977	33107863	8	~1985
5518397	33110383	8	~1985
5518913	1898506073	10	~1989
5519159	11038319	8	~1984
5519299	99347383	8	~1986
5519447	44155577	8	~1985
5519453	33116719	8	~1985
5519639	99353503	8	~1986
5520017	33120103	8	~1985
5520059	11040119	8	~1984
5520083	11040167	8	~1984
5520191	11040383	8	~1984
5520323	11040647	8	~1984
5520421	33122527	8	~1985
5520553	33123319	8	~1985
5520677	44165417	8	~1985
5520769	5068065943	10	~1990
5520791	99374239	8	~1986
5520863	11041727	8	~1984
5520913	132501913	9	~1986

Exp.	Prime Factor	Digits	Year
5520923	11041847	8	~1984
5521133	33126799	8	~1985
5521181	44169449	8	~1985
5521199	11042399	8	~1984
5521213	88339409	8	~1986
5521301	397533673	9	~1987
5521559	11043119	8	~1984
5521693	88347089	8	~1986
5521697	33130183	8	~1985
5521981	1446759023	10	~1989
5522039	44176313	8	~1985
5522063	11044127	8	~1984
5522137	33132823	8	~1985
5522203	88355249	8	~1986
5522261	33133567	8	~1985
5522281	33133687	8	~1985
5522393	33134359	8	~1985
5522411	11044823	8	~1984
5522519	11045039	8	~1984
5522527	132540649	9	~1986
5522999	11045999	8	~1984
5523131	44185049	8	~1985
5523481	88375697	8	~1986
5523541	33141247	8	~1985
5524159	132579817	9	~1986

Exp.	Prime Factor	Digits	Year
5524219	55242191	8	~1985
5524279	55242791	8	~1985
5524331	11048663	8	~1984
5524357	33146143	8	~1985
5524513	88392209	8	~1986
5524523	11049047	8	~1984
5524691	11049383	8	~1984
5524691	44197529	8
5525053	33150319	8	~1985
5525087	143652263	9	~1986
5525183	11050367	8	~1984
5525183	176805857	9
5525251	265212049	9	~1987
5525453	77356343	8	~1986
5525519	11051039	8	~1984
5525581	33153487	8	~1985
5525777	77360879	8	~1986
5525797	33154783	8	~1985
5526041	33156247	8	~1985
5526043	55260431	8	~1985
5526113	33156679	8	~1985
5526137	77365919	8	~1986
5526179	11052359	8	~1984
5526481	33158887	8	~1985
5526613	132638713	9	~1986

5.307.017 digits

26-01-11