Small Mersenne Prime Factors (page 812/5670)

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
6351563	12703127	8	~1984
6351953	38111719	8	~1985
6352331	12704663	8	~1984
6352487	50819897	8	~1986
6352987	63529871	8	~1986
6353003	12706007	8	~1984
6353093	38118559	8	~1985
6353351	12706703	8	~1984
6353741	50829929	8	~1986
6353783	12707567	8	~1984
6353857	38123143	8	~1985
6354017	38124103	8	~1985
6354059	50832473	8	~1986
6354119	12708239	8	~1984
6354421	38126527	8	~1985
6354599	12709199	8	~1984
6354619	63546191	8	~1986
6354703	63547031	8	~1986
6354827	114386887	9	~1986
6355039	63550391	8	~1986
6355243	63552431	8	~1986
6355597	38133583	8	~1985
6355631	12711263	8	~1984
6355711	63557111	8	~1986
6356039	12712079	8	~1984

Exp.	Prime Factor	Digits	Year
6356087	50848697	8	~1986
6356243	12712487	8	~1984
6356243	317812151	9
6356309	50850473	8	~1986
6356401	38138407	8	~1985
6356543	12713087	8	~1984
6356639	12713279	8	~1984
6356641	38139847	8	~1985
6357083	12714167	8	~1984
6357317	50858537	8	~1986
6357907	114442327	9	~1986
6357929	152590297	9	~1987
6358003	101728049	9	~1986
6358031	12716063	8	~1984
6358057	38148343	8	~1985
6358139	12716279	8	~1984
6358151	12716303	8	~1984
6358211	12716423	8	~1984
6358481	50867849	8	~1986
6358553	190756591	9	~1987
6358571	50868569	8	~1986
6358619	12717239	8	~1984
6358621	38151727	8	~1985
6358753	38152519	8	~1985
6358777	38152663	8	~1985

Exp.	Prime Factor	Digits	Year
6358991	12717983	8	~1984
6359159	12718319	8	~1984
6359279	152622697	9	~1987
6359393	38156359	8	~1985
6359537	50876297	8	~1986
6359803	572382271	9	~1988
6359957	546956303	9	~1988
6359981	50879849	8	~1986
6360427	63604271	8	~1986
6360437	38162623	8	~1985
6360551	12721103	8	~1984
6360553	38163319	8	~1985
6360593	152654233	9	~1987
6360899	12721799	8	~1984
6360923	12721847	8	~1984
6361073	38166439	8	~1985
6361079	12722159	8	~1984
6361367	50890937	8	~1986
6361651	101786417	9	~1986
6362171	12724343	8	~1984
6362231	12724463	8	~1984
6362399	12724799	8	~1984
6362519	12725039	8	~1984
6362591	12725183	8	~1984
6362633	38175799	8	~1985

Exp.	Prime Factor	Digits	Year
6362659	216330407	9	~1987
6362669	50901353	8	~1986
6362791	63627911	8	~1986
6362833	101805329	9	~1986
6362957	38177743	8	~1985
6363073	610855009	9	~1988
6363169	139989719	9	~1987
6363359	12726719	8	~1984
6363503	12727007	8	~1984
6363601	254544041	9	~1987
6363653	38181919	8	~1985
6363761	38182567	8	~1985
6363881	38183287	8	~1985
6363997	38183983	8	~1985
6364381	38186287	8	~1985
6364691	12729383	8	~1984
6364727	50917817	8	~1986
6364751	12729503	8	~1984
6365003	12730007	8	~1984
6365071	254602841	9	~1987
6365081	38190487	8	~1985
6365377	305538097	9	~1988
6365699	12731399	8	~1984
6365699	50925593	8
6365717	50925737	8	~1986

5.366.787 digits

26-02-08