Small Mersenne Prime Factors (page 931/5670)

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
8008597	48051583	8	~1986
8008877	48053263	8	~1986
8009009	256288289	9	~1988
8009219	16018439	8	~1985
8009291	400464551	9	~1988
8009293	48055759	8	~1986
8009759	16019519	8	~1985
8009893	48059359	8	~1986
8009929	176218439	9	~1987
8009999	16019999	8	~1985
8010011	16020023	8	~1985
8010113	48060679	8	~1986
8010239	16020479	8	~1985
8010251	16020503	8	~1985
8010263	16020527	8	~1985
8010481	48062887	8	~1986
8010481	176230583	9
8010839	16021679	8	~1985
8010839	64086713	8
8010853	48065119	8	~1986
8011007	144198127	9	~1987
8011261	48067567	8	~1986
8011319	16022639	8	~1985
8011937	48071623	8	~1986
8011967	208311143	9	~1988

Exp.	Prime Factor	Digits	Year
8012003	16024007	8	~1985
8012383	80123831	8	~1987
8012519	16025039	8	~1985
8012791	80127911	8	~1987
8012801	48076807	8	~1986
8012959	80129591	8	~1987
8013329	384639793	9	~1988
8013487	80134871	8	~1987
8013521	48081127	8	~1986
8013623	16027247	8	~1985
8013659	64109273	8	~1986
8013757	48082543	8	~1986
8014033	48084199	8	~1986
8014141	48084847	8	~1986
8014343	16028687	8	~1985
8014427	64115417	8	~1986
8014679	16029359	8	~1985
8015303	16030607	8	~1985
8015531	16031063	8	~1985
8015543	16031087	8	~1985
8015591	64124729	8	~1986
8015659	80156591	8	~1987
8015719	80157191	8	~1987
8015723	16031447	8	~1985
8015783	16031567	8	~1985

Exp.	Prime Factor	Digits	Year
8016191	16032383	8	~1985
8016479	64131833	8	~1986
8016611	16033223	8	~1985
8016661	48099967	8	~1986
8016779	16033559	8	~1985
8016923	16033847	8	~1985
8017117	513095489	9	~1989
8017439	64139513	8	~1986
8017571	6542337937	10	~1991
8017643	16035287	8	~1985
8017739	16035479	8	~1985
8017819	80178191	8	~1987
8017951	80179511	8	~1987
8017993	48107959	8	~1986
8018047	128288753	9	~1987
8018183	16036367	8	~1985
8018189	64145513	8	~1986
8018291	16036583	8	~1985
8018453	48110719	8	~1986
8018963	16037927	8	~1985
8019001	48114007	8	~1986
8019023	16038047	8	~1985
8019041	48114247	8	~1986
8019611	16039223	8	~1985
8019773	48118639	8	~1986

Exp.	Prime Factor	Digits	Year
8020151	16040303	8	~1985
8020339	80203391	8	~1987
8020499	64163993	8	~1986
8020577	384987697	9	~1988
8020643	16041287	8	~1985
8020673	48124039	8	~1986
8020703	16041407	8	~1985
8020921	48125527	8	~1986
8020927	80209271	8	~1987
8020933	48125599	8	~1986
8020933	128334929	9
8021003	16042007	8	~1985
8021063	914401183	9	~1989
8021131	144380359	9	~1987
8021159	16042319	8	~1985
8021171	16042343	8	~1985
8021291	16042583	8	~1985
8021471	64171769	8	~1986
8021593	48129559	8	~1986
8021647	128346353	9	~1987
8021831	16043663	8	~1985
8021911	144394399	9	~1987
8022017	48132103	8	~1986
8022061	128352977	9	~1987
8022083	16044167	8	~1985

5.366.787 digits

26-02-08