Small Mersenne Prime Factors (page 777/5025)

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
6285841	37715047	8	~1985
6285931	62859311	8	~1986
6286019	50288153	8	~1986
6286229	150869497	9	~1987
6286331	12572663	8	~1984
6286339	62863391	8	~1986
6286507	62865071	8	~1986
6286697	37720183	8	~1985
6287033	37722199	8	~1985
6287179	62871791	8	~1986
6287273	37723639	8	~1985
6287459	50299673	8	~1986
6287573	37725439	8	~1985
6287581	37725487	8	~1985
6287639	12575279	8	~1984
6287783	12575567	8	~1984
6287849	50302793	8	~1986
6287893	37727359	8	~1985
6288119	50304953	8	~1986
6288199	817465871	9	~1989
6288311	12576623	8	~1984
6288313	138342887	9	~1987
6288323	12576647	8	~1984
6288349	150920377	9	~1987
6288511	62885111	8	~1986

Exp.	Prime Factor	Digits	Year
6288613	37731679	8	~1985
6288781	37732687	8	~1985
6288781	100620497	9
6289091	12578183	8	~1984
6289229	50313833	8	~1986
6289237	150941689	9	~1987
6289469	50315753	8	~1986
6289601	50316809	8	~1986
6289697	50317577	8	~1986
6289783	62897831	8	~1986
6289841	37739047	8	~1985
6289939	62899391	8	~1986
6289957	37739743	8	~1985
6290021	50320169	8	~1986
6290243	12580487	8	~1984
6290327	50322617	8	~1986
6290633	37743799	8	~1985
6290693	37744159	8	~1985
6290759	12581519	8	~1984
6290951	12581903	8	~1984
6291277	37747663	8	~1985
6291487	553650857	9	~1988
6291503	12583007	8	~1984
6291529	150996697	9	~1987
6291529	704651249	9

Exp.	Prime Factor	Digits	Year
6291757	37750543	8	~1985
6291773	37750639	8	~1985
6291863	201339617	9	~1987
6291911	163589687	9	~1987
6291941	50335529	8	~1986
6291959	12583919	8	~1984
6291973	37751839	8	~1985
6292417	37754503	8	~1985
6292441	100679057	9	~1986
6292543	62925431	8	~1986
6292813	37756879	8	~1985
6292981	37757887	8	~1985
6293291	12586583	8	~1984
6293597	50348777	8	~1986
6293939	12587879	8	~1984
6294083	12588167	8	~1984
6294137	37764823	8	~1985
6294143	12588287	8	~1984
6294161	37764967	8	~1985
6294251	12588503	8	~1984
6294311	12588623	8	~1984
6294721	37768327	8	~1985
6294779	12589559	8	~1984
6294971	50359769	8	~1986
6294973	37769839	8	~1985

Exp.	Prime Factor	Digits	Year
6295043	12590087	8	~1984
6295109	50360873	8	~1986
6295277	37771663	8	~1985
6295337	37772023	8	~1985
6295481	50363849	8	~1986
6295577	50364617	8	~1986
6295657	37773943	8	~1985
6295769	50366153	8	~1986
6295879	264426919	9	~1987
6296141	37776847	8	~1985
6296159	50369273	8	~1986
6296377	37778263	8	~1985
6296573	37779439	8	~1985
6296651	503732081	9	~1988
6296831	12593663	8	~1984
6296833	37780999	8	~1985
6297383	12594767	8	~1984
6297419	12594839	8	~1984
6297419	50379353	8
6297763	62977631	8	~1986
6297997	37787983	8	~1985
6298079	12596159	8	~1984
6298163	12596327	8	~1984
6298199	12596399	8	~1984
6298393	37790359	8	~1985

4.724.182 digits

25-04-13