Small Mersenne Prime Factors (page 704/5550)

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
5053889	40431113	8	~1985
5054053	30324319	8	~1985
5054267	131410943	9	~1986
5054351	40434809	8	~1985
5054417	40435337	8	~1985
5054431	293156999	9	~1987
5054531	10109063	8	~1983
5054639	10109279	8	~1983
5054677	30328063	8	~1985
5054713	30328279	8	~1985
5054989	323519297	9	~1987
5055023	10110047	8	~1983
5055053	30330319	8	~1985
5055059	10110119	8	~1983
5055107	40440857	8	~1985
5055191	10110383	8	~1983
5055359	40442873	8	~1985
5055551	10111103	8	~1983
5055623	10111247	8	~1983
5055667	121336009	9	~1986
5055923	10111847	8	~1983
5056217	40449737	8	~1985
5056397	3468688343	10	~1990
5056567	80905073	8	~1986
5056577	40452617	8	~1985

Exp.	Prime Factor	Digits	Year
5056577	70792079	8
5056697	40453577	8	~1985
5056739	10113479	8	~1983
5056823	10113647	8	~1983
5056979	10113959	8	~1983
5057099	10114199	8	~1983
5057471	10114943	8	~1983
5057639	10115279	8	~1983
5057797	30346783	8	~1985
5057851	50578511	8	~1985
5057963	10115927	8	~1983
5058023	10116047	8	~1983
5058083	10116167	8	~1983
5058329	40466633	8	~1985
5058491	10116983	8	~1983
5058511	91053199	8	~1986
5058569	40468553	8	~1985
5058631	50586311	8	~1985
5058721	111291863	9	~1986
5058881	30353287	8	~1985
5058917	30353503	8	~1985
5059283	10118567	8	~1983
5059291	50592911	8	~1985
5059507	50595071	8	~1985
5059679	10119359	8	~1983

Exp.	Prime Factor	Digits	Year
5059679	40477433	8
5059679	374416247	9
5059919	40479353	8	~1985
5059937	40479497	8	~1985
5059961	30359767	8	~1985
5059979	10119959	8	~1983
5060171	10120343	8	~1983
5060431	50604311	8	~1985
5060591	10121183	8	~1983
5060609	121454617	9	~1986
5060771	10121543	8	~1983
5060791	50607911	8	~1985
5061031	50610311	8	~1985
5061107	40488857	8	~1985
5061263	10122527	8	~1983
5061493	30368959	8	~1985
5061599	10123199	8	~1983
5061827	40494617	8	~1985
5062091	10124183	8	~1983
5062163	10124327	8	~1983
5062237	30373423	8	~1985
5062621	718892183	9	~1988
5062633	30375799	8	~1985
5062661	151879831	9	~1986
5062697	40501577	8	~1985

Exp.	Prime Factor	Digits	Year
5062859	10125719	8	~1983
5063033	30378199	8	~1985
5063039	10126079	8	~1983
5063111	10126223	8	~1983
5063141	243030769	9	~1987
5063389	324056897	9	~1987
5063431	91141759	8	~1986
5063489	40507913	8	~1985
5063843	10127687	8	~1983
5063879	10127759	8	~1983
5064043	334226839	9	~1987
5064167	40513337	8	~1985
5064263	131670839	9	~1986
5064263	253213151	9
5064341	30386047	8	~1985
5064373	81029969	8	~1986
5064539	10129079	8	~1983
5064551	10129103	8	~1983
5064599	10129199	8	~1983
5064601	30387607	8	~1985
5064629	40517033	8	~1985
5064713	30388279	8	~1985
5064727	50647271	8	~1985
5064881	40519049	8	~1985
5065019	10130039	8	~1983

5.247.179 digits

25-12-14