Small Mersenne Prime Factors (page 898/5550)

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
7621217	60969737	8	~1986
7621547	60972377	8	~1986
7621619	60972953	8	~1986
7621843	76218431	8	~1986
7622291	15244583	8	~1985
7622399	15244799	8	~1985
7622663	15245327	8	~1985
7622779	320156719	9	~1988
7622837	45737023	8	~1986
7622873	45737239	8	~1986
7623037	121968593	9	~1987
7623137	106723919	9	~1987
7623229	167711039	9	~1987
7623311	60986489	8	~1986
7623359	15246719	8	~1985
7623403	121974449	9	~1987
7623661	45741967	8	~1986
7623779	15247559	8	~1985
7624033	121984529	9	~1987
7624139	60993113	8	~1986
7624271	15248543	8	~1985
7624433	45746599	8	~1986
7624457	60995657	8	~1986
7624649	60997193	8	~1986
7624691	15249383	8	~1985

Exp.	Prime Factor	Digits	Year
7624691	60997529	8
7624831	137246959	9	~1987
7624913	45749479	8	~1986
7625323	305012921	9	~1988
7625357	61002857	8	~1986
7625363	15250727	8	~1985
7625603	15251207	8	~1985
7625621	45753727	8	~1986
7625699	15251399	8	~1985
7625701	45754207	8	~1986
7625789	61006313	8	~1986
7625939	15251879	8	~1985
7626119	15252239	8	~1985
7626313	228789391	9	~1988
7626629	61013033	8	~1986
7626667	122026673	9	~1987
7627063	76270631	8	~1986
7627093	45762559	8	~1986
7627199	15254399	8	~1985
7627393	45764359	8	~1986
7627589	244082849	9	~1988
7627943	198326519	9	~1987
7627979	15255959	8	~1985
7628069	61024553	8	~1986
7628221	45769327	8	~1986

Exp.	Prime Factor	Digits	Year
7628339	15256679	8	~1985
7628399	15256799	8	~1985
7628591	15257183	8	~1985
7628627	137315287	9	~1987
7628681	45772087	8	~1986
7628867	183092809	9	~1987
7629071	15258143	8	~1985
7629179	61033433	8	~1986
7629299	15258599	8	~1985
7629851	15259703	8	~1985
7630067	61040537	8	~1986
7630081	45780487	8	~1986
7630211	15260423	8	~1985
7630477	122087633	9	~1987
7630589	549402409	9	~1989
7630643	15261287	8	~1985
7630789	1144618351	10	~1989
7630817	45784903	8	~1986
7631051	15262103	8	~1985
7631381	45788287	8	~1986
7631489	106840847	9	~1987
7631537	61052297	8	~1986
7631551	76315511	8	~1986
7631761	45790567	8	~1986
7631831	15263663	8	~1985

Exp.	Prime Factor	Digits	Year
7631881	45791287	8	~1986
7631951	61055609	8	~1986
7632011	15264023	8	~1985
7632011	61056089	8
7632059	61056473	8	~1986
7632143	15264287	8	~1985
7632533	45795199	8	~1986
7632641	45795847	8	~1986
7632719	61061753	8	~1986
7632971	137393479	9	~1987
7633091	15266183	8	~1985
7633091	137395639	9
7633627	49649110009	11	~1993
7633679	15267359	8	~1985
7633679	61069433	8
7633859	15267719	8	~1985
7633859	61070873	8
7634093	45804559	8	~1986
7634113	45804679	8	~1986
7634357	61074857	8	~1986
7634441	45806647	8	~1986
7634519	15269039	8	~1985
7634719	76347191	8	~1986
7634969	106889567	9	~1987
7635059	15270119	8	~1985

5.247.179 digits

25-12-14