Small Mersenne Prime Factors (page 797/5460)

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
6274993	37649959	8	~1985
6275603	150614473	9	~1987
6275701	37654207	8	~1985
6275821	37654927	8	~1985
6275891	12551783	8	~1984
6275953	37655719	8	~1985
6276131	12552263	8	~1984
6276497	50211977	8	~1986
6276563	12553127	8	~1984
6276671	50213369	8	~1986
6276841	37661047	8	~1985
6277001	50216009	8	~1986
6277027	112986487	9	~1986
6277339	150656137	9	~1987
6277361	37664167	8	~1985
6277451	12554903	8	~1984
6277559	12555119	8	~1984
6277639	62776391	8	~1986
6277727	50221817	8	~1986
6278053	100448849	9	~1986
6278099	12556199	8	~1984
6278179	62781791	8	~1986
6278231	12556463	8	~1984
6278243	12556487	8	~1984
6278497	188354911	9	~1987

Exp.	Prime Factor	Digits	Year
6278513	200912417	9	~1987
6278527	62785271	8	~1986
6278561	37671367	8	~1985
6278681	37672087	8	~1985
6279197	50233577	8	~1986
6279257	50234057	8	~1986
6279263	12558527	8	~1984
6279551	12559103	8	~1984
6279803	12559607	8	~1984
6279941	37679647	8	~1985
6280091	12560183	8	~1984
6280147	62801471	8	~1986
6280441	37682647	8	~1985
6280511	12561023	8	~1984
6280777	37684663	8	~1985
6281161	37686967	8	~1985
6281239	62812391	8	~1986
6281339	12562679	8	~1984
6281459	12562919	8	~1984
6281519	12563039	8	~1984
6281579	263826319	9	~1987
6281591	12563183	8	~1984
6281909	201021089	9	~1987
6282071	12564143	8	~1984
6282377	50259017	8	~1986

Exp.	Prime Factor	Digits	Year
6282961	100527377	9	~1986
6283019	50264153	8	~1986
6283157	37698943	8	~1985
6283253	87965543	8	~1986
6283273	37699639	8	~1985
6283331	12566663	8	~1984
6283379	12566759	8	~1984
6283811	12567623	8	~1984
6283841	50270729	8	~1986
6284017	37704103	8	~1985
6284123	12568247	8	~1984
6284527	62845271	8	~1986
6284549	50276393	8	~1986
6284717	37708303	8	~1985
6284903	12569807	8	~1984
6285277	100564433	9	~1986
6285527	113139487	9	~1986
6285557	50284457	8	~1986
6285613	37713679	8	~1985
6285659	12571319	8	~1984
6285791	12571583	8	~1984
6285841	37715047	8	~1985
6285931	62859311	8	~1986
6286019	50288153	8	~1986
6286229	150869497	9	~1987

Exp.	Prime Factor	Digits	Year
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
6288613	37731679	8	~1985
6288781	37732687	8	~1985
6288781	100620497	9
6288941	603738337	9	~1988

5.157.210 digits

25-11-02