Small Mersenne Prime Factors (page 1004/5610)

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
9155123	18310247	8	~1985
9155351	18310703	8	~1985
9155351	73242809	8
9155411	18310823	8	~1985
9155543	18311087	8	~1985
9155759	73246073	8	~1987
9155897	54935383	8	~1987
9156341	73250729	8	~1987
9156551	18313103	8	~1985
9156611	18313223	8	~1985
9156887	73255097	8	~1987
9157139	73257113	8	~1987
9157451	18314903	8	~1985
9158003	18316007	8	~1985
9158161	54948967	8	~1987
9158197	54949183	8	~1987
9158231	73265849	8	~1987
9158717	219809209	9	~1988
9158783	18317567	8	~1985
9158993	54953959	8	~1987
9159247	146547953	9	~1988
9159431	18318863	8	~1985
9159487	91594871	8	~1987
9159599	18319199	8	~1985
9159859	164877463	9	~1988

Exp.	Prime Factor	Digits	Year
9160031	18320063	8	~1985
9160357	54962143	8	~1987
9160379	73283033	8	~1987
9160421	54962527	8	~1987
9160439	18320879	8	~1985
9160483	91604831	8	~1987
9160499	73283993	8	~1987
9160643	18321287	8	~1985
9160661	54963967	8	~1987
9160721	73285769	8	~1987
9161167	366446681	9	~1989
9161171	73289369	8	~1987
9161261	73290089	8	~1987
9161543	659631097	9	~1989
9161597	54969583	8	~1987
9161729	73293833	8	~1987
9161897	54971383	8	~1987
9162037	54972223	8	~1987
9162563	18325127	8	~1985
9162653	54975919	8	~1987
9163079	18326159	8	~1985
9163403	18326807	8	~1985
9163559	18327119	8	~1985
9164191	91641911	8	~1987
9164333	54985999	8	~1987

Exp.	Prime Factor	Digits	Year
9164417	73315337	8	~1987
9164471	18328943	8	~1985
9164681	879809377	9	~1989
9164843	18329687	8	~1985
9164951	18329903	8	~1985
9165083	18330167	8	~1985
9165179	18330359	8	~1985
9165257	54991543	8	~1987
9165323	18330647	8	~1985
9165683	18331367	8	~1985
9165797	54994783	8	~1987
9165833	54994999	8	~1987
9165917	73327337	8	~1987
9166211	18332423	8	~1985
9166499	18332999	8	~1985
9166517	128331239	9	~1987
9166763	18333527	8	~1985
9166823	18333647	8	~1985
9166931	18333863	8	~1985
9166967	220007209	9	~1988
9166973	55001839	8	~1987
9167167	146674673	9	~1988
9167371	91673711	8	~1987
9167441	55004647	8	~1987
9167531	73340249	8	~1987

Exp.	Prime Factor	Digits	Year
9167531	165015559	9
9167771	18335543	8	~1985
9168011	18336023	8	~1985
9168077	55008463	8	~1987
9168217	55009303	8	~1987
9168251	18336503	8	~1985
9168623	18337247	8	~1985
9168671	18337343	8	~1985
9169063	91690631	8	~1987
9169529	73356233	8	~1987
9169619	18339239	8	~1985
9170363	18340727	8	~1985
9170417	73363337	8	~1987
9170549	73364393	8	~1987
9170809	220099417	9	~1988
9171131	18342263	8	~1985
9171307	91713071	8	~1987
9171731	18343463	8	~1985
9171881	55031287	8	~1987
9171907	91719071	8	~1987
9171971	18343943	8	~1985
9172057	495291079	9	~1989
9172133	55032799	8	~1987
9172211	18344423	8	~1985
9172343	18344687	8	~1985

5.307.017 digits

26-01-11