Small Mersenne Prime Factors (page 927/5460)

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
8125639	715056233	9	~1989
8125811	16251623	8	~1985
8125823	16251647	8	~1985
8126009	390048433	9	~1988
8126087	406304351	9	~1988
8126137	195027289	9	~1988
8126213	48757279	8	~1986
8126711	16253423	8	~1985
8126879	65015033	8	~1986
8127023	16254047	8	~1985
8127083	16254167	8	~1985
8127233	48763399	8	~1986
8127271	130036337	9	~1987
8127293	113782103	9	~1987
8127313	48763879	8	~1986
8127551	16255103	8	~1985
8127923	16255847	8	~1985
8129081	48774487	8	~1986
8129123	16258247	8	~1985
8129221	390202609	9	~1988
8129339	65034713	8	~1986
8129411	536541127	9	~1989
8129413	48776479	8	~1986
8129477	48776863	8	~1986
8129507	65036057	8	~1986

Exp.	Prime Factor	Digits	Year
8129783	16259567	8	~1985
8129939	16259879	8	~1985
8130581	65044649	8	~1986
8130599	195134377	9	~1988
8130673	130090769	9	~1987
8130851	16261703	8	~1985
8130911	16261823	8	~1985
8131241	48787447	8	~1986
8131337	48788023	8	~1986
8131633	48789799	8	~1986
8131961	48791767	8	~1986
8132051	16264103	8	~1985
8132219	16264439	8	~1985
8132291	16264583	8	~1985
8132347	130117553	9	~1987
8132483	16264967	8	~1985
8132759	16265519	8	~1985
8132843	16265687	8	~1985
8133241	130131857	9	~1987
8133371	16266743	8	~1985
8133403	81334031	8	~1987
8133791	16267583	8	~1985
8133971	16267943	8	~1985
8134739	16269479	8	~1985
8134799	16269599	8	~1985

Exp.	Prime Factor	Digits	Year
8134949	65079593	8	~1986
8135201	48811207	8	~1986
8135221	48811327	8	~1986
8135243	16270487	8	~1985
8135279	16270559	8	~1985
8135279	65082233	8
8135581	48813487	8	~1986
8135797	48814783	8	~1986
8136143	16272287	8	~1985
8136551	65092409	8	~1986
8136743	16273487	8	~1985
8137411	130198577	9	~1987
8137517	48825103	8	~1986
8137609	179027399	9	~1988
8137631	16275263	8	~1985
8137813	48826879	8	~1986
8138111	16276223	8	~1985
8138363	16276727	8	~1985
8138539	81385391	8	~1987
8138579	16277159	8	~1985
8138861	65110889	8	~1986
8138863	276721343	9	~1988
8139119	16278239	8	~1985
8139359	16278719	8	~1985
8139431	16278863	8	~1985

Exp.	Prime Factor	Digits	Year
8139553	48837319	8	~1986
8139917	48839503	8	~1986
8139959	16279919	8	~1985
8140133	195363193	9	~1988
8140211	16280423	8	~1985
8140211	65121689	8
8140439	16280879	8	~1985
8140571	16281143	8	~1985
8140661	65125289	8	~1986
8141059	81410591	8	~1987
8141569	179114519	9	~1988
8141879	16283759	8	~1985
8141891	16283783	8	~1985
8141957	195406969	9	~1988
8142221	65137769	8	~1986
8142307	81423071	8	~1987
8142353	48854119	8	~1986
8142503	16285007	8	~1985
8142731	16285463	8	~1985
8142817	48856903	8	~1986
8143151	65145209	8	~1986
8143199	65145593	8	~1986
8143231	130291697	9	~1987
8143237	48859423	8	~1986
8143273	48859639	8	~1986

5.157.210 digits

25-11-02