Small Mersenne Prime Factors (page 705/5025)

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
5346631	53466311	8	~1985
5346743	171095777	9	~1986
5346763	85548209	8	~1986
5346779	10693559	8	~1984
5346791	10693583	8	~1984
5346877	32081263	8	~1985
5346989	42775913	8	~1985
5347211	10694423	8	~1984
5347211	42777689	8
5347403	10694807	8	~1984
5347411	53474111	8	~1985
5347619	10695239	8	~1984
5348153	32088919	8	~1985
5348159	10696319	8	~1984
5348249	42785993	8	~1985
5348261	42786089	8	~1985
5348363	10696727	8	~1984
5348449	160453471	9	~1986
5348923	53489231	8	~1985
5349083	10698167	8	~1984
5349191	10698383	8	~1984
5349299	10698599	8	~1984
5349437	42795497	8	~1985
5349671	10699343	8	~1984
5349739	53497391	8	~1985

Exp.	Prime Factor	Digits	Year
5349797	74897159	8	~1986
5349857	42798857	8	~1985
5349901	32099407	8	~1985
5350139	10700279	8	~1984
5350199	10700399	8	~1984
5350201	117704423	9	~1986
5350333	32101999	8	~1985
5350391	10700783	8	~1984
5350463	10700927	8	~1984
5350649	42805193	8	~1985
5350831	53508311	8	~1985
5350883	10701767	8	~1984
5350931	10701863	8	~1984
5350967	96317407	8	~1986
5351077	32106463	8	~1985
5351147	42809177	8	~1985
5351237	74917319	8	~1986
5351287	53512871	8	~1985
5351299	310375343	9	~1987
5351321	42810569	8	~1985
5351459	10702919	8	~1984
5351531	42812249	8	~1985
5351579	10703159	8	~1984
5351609	42812873	8	~1985
5351761	32110567	8	~1985

Exp.	Prime Factor	Digits	Year
5351783	513771169	9	~1988
5352001	32112007	8	~1985
5352071	10704143	8	~1984
5352121	32112727	8	~1985
5352199	770716657	9	~1988
5352239	10704479	8	~1984
5352359	42818873	8	~1985
5352419	96343543	8	~1986
5352439	53524391	8	~1985
5352551	10705103	8	~1984
5352731	10705463	8	~1984
5352911	10705823	8	~1984
5352913	85646609	8	~1986
5353259	42826073	8	~1985
5353399	96361183	8	~1986
5353693	32122159	8	~1985
5353811	10707623	8	~1984
5353883	2923220119	10	~1989
5354071	96373279	8	~1986
5354443	53544431	8	~1985
5354953	85679249	8	~1986
5355011	10710023	8	~1984
5355211	53552111	8	~1985
5355257	32131543	8	~1985
5355271	1756528889	10	~1989

Exp.	Prime Factor	Digits	Year
5355419	10710839	8	~1984
5355433	32132599	8	~1985
5355487	53554871	8	~1985
5355503	10711007	8	~1984
5355683	10711367	8	~1984
5355851	10711703	8	~1984
5356051	53560511	8	~1985
5356067	128545609	9	~1986
5356133	74985863	8	~1986
5356303	53563031	8	~1985
5356607	42852857	8	~1985
5356621	32139727	8	~1985
5356697	74993759	8	~1986
5356943	10713887	8	~1984
5356979	10713959	8	~1984
5356979	42855833	8
5357003	10714007	8	~1984
5357123	10714247	8	~1984
5357237	42857897	8	~1985
5357441	42859529	8	~1985
5357657	32145943	8	~1985
5357719	53577191	8	~1985
5357831	42862649	8	~1985
5357879	10715759	8	~1984
5357903	10715807	8	~1984

4.724.182 digits

25-04-13