Small Mersenne Prime Factors (page 916/5745)

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
7730651	200996927	9	~1988
7730963	695786671	9	~1989
7731433	46388599	8	~1986
7731707	432975593	9	~1988
7731721	46390327	8	~1986
7731761	46390567	8	~1986
7731881	61855049	8	~1986
7732321	46393927	8	~1986
7732457	46394743	8	~1986
7732471	77324711	8	~1987
7732633	46395799	8	~1986
7733087	61864697	8	~1986
7733321	61866569	8	~1986
7733431	77334311	8	~1987
7733471	15466943	8	~1985
7733711	15467423	8	~1985
7733941	46403647	8	~1986
7733951	61871609	8	~1986
7733983	77339831	8	~1987
7734119	15468239	8	~1985
7734203	15468407	8	~1985
7734317	61874537	8	~1986
7734607	139222927	9	~1987
7734689	61877513	8	~1986
7734791	15469583	8	~1985

Exp.	Prime Factor	Digits	Year
7734827	61878617	8	~1986
7734911	61879289	8	~1986
7734971	15469943	8	~1985
7735163	15470327	8	~1985
7735319	15470639	8	~1985
7735361	46412167	8	~1986
7735439	15470879	8	~1985
7735583	15471167	8	~1985
7735597	46413583	8	~1986
7735811	15471623	8	~1985
7736593	46419559	8	~1986
7736627	510617383	9	~1989
7736633	46419799	8	~1986
7736761	46420567	8	~1986
7736831	15473663	8	~1985
7736831	61894649	8
7736873	46421239	8	~1986
7736951	15473903	8	~1985
7737071	15474143	8	~1985
7737263	15474527	8	~1985
7737677	61901417	8	~1986
7737967	77379671	8	~1987
7738271	15476543	8	~1985
7738337	46430023	8	~1986
7738337	61906697	8

Exp.	Prime Factor	Digits	Year
7738427	371444497	9	~1988
7738457	294061367	9	~1988
7738943	15477887	8	~1985
7739101	46434607	8	~1986
7739189	61913513	8	~1986
7739273	433399289	9	~1988
7739519	15479039	8	~1985
7739597	46437583	8	~1986
7739651	61917209	8	~1986
7739843	15479687	8	~1985
7740023	928802761	9	~1989
7740119	15480239	8	~1985
7740203	15480407	8	~1985
7740547	309621881	9	~1988
7740599	15481199	8	~1985
7740611	15481223	8	~1985
7740833	46444999	8	~1986
7741403	15482807	8	~1985
7742411	15484823	8	~1985
7742459	15484919	8	~1985
7742677	46456063	8	~1986
7742723	15485447	8	~1985
7742771	15485543	8	~1985
7742807	61942457	8	~1986
7742957	61943657	8	~1986

Exp.	Prime Factor	Digits	Year
7742957	108401399	9
7743209	61945673	8	~1986
7743389	61947113	8	~1986
7743409	495578177	9	~1988
7743503	15487007	8	~1985
7743559	77435591	8	~1987
7743611	61948889	8	~1986
7743731	247799393	9	~1988
7744151	61953209	8	~1986
7744391	15488783	8	~1985
7744403	15488807	8	~1985
7744631	15489263	8	~1985
7744631	325274503	9
7744657	46467943	8	~1986
7744739	15489479	8	~1985
7744831	371751889	9	~1988
7745033	46470199	8	~1986
7745051	15490103	8	~1985
7745819	15491639	8	~1985
7746083	15492167	8	~1985
7746133	46476799	8	~1986
7746241	46477447	8	~1986
7746449	61971593	8	~1986
7746569	61972553	8	~1986
7746863	15493727	8	~1985

5.441.361 digits

26-03-15