Small Mersenne Prime Factors (page 877/5025)

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
7744631	15489263	8	~1985
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
7747001	61976009	8	~1986
7747037	294387407	9	~1988
7747093	46482559	8	~1986
7747217	46483303	8	~1986
7747511	557820793	9	~1989
7747561	46485367	8	~1986
7747643	15495287	8	~1985
7747673	247925537	9	~1988
7747739	15495479	8	~1985
7747819	139460743	9	~1987
7747933	46487599	8	~1986
7747981	46487887	8	~1986

Exp.	Prime Factor	Digits	Year
7748009	108472127	9	~1987
7748099	15496199	8	~1985
7748113	46488679	8	~1986
7748261	46489567	8	~1986
7748459	15496919	8	~1985
7748627	61989017	8	~1986
7748831	15497663	8	~1985
7748921	46493527	8	~1986
7748921	371948209	9
7749227	61993817	8	~1986
7749251	15498503	8	~1985
7749299	15498599	8	~1985
7749353	46496119	8	~1986
7749491	15498983	8	~1985
7749517	46497103	8	~1986
7749611	61996889	8	~1986
7749799	681982313	9	~1989
7749803	15499607	8	~1985
7749887	61999097	8	~1986
7750097	62000777	8	~1986
7750121	232503631	9	~1988
7750201	46501207	8	~1986
7750559	15501119	8	~1985
7750711	325529863	9	~1988
7750913	46505479	8	~1986

Exp.	Prime Factor	Digits	Year
7751101	232533031	9	~1988
7751123	15502247	8	~1985
7751279	62010233	8	~1986
7751551	325565143	9	~1988
7751591	62012729	8	~1986
7751963	15503927	8	~1985
7752131	15504263	8	~1985
7752161	46512967	8	~1986
7752293	46513759	8	~1986
7752373	46514239	8	~1986
7752517	46515103	8	~1986
7752539	15505079	8	~1985
7752683	15505367	8	~1985
7753177	46519063	8	~1986
7753673	46522039	8	~1986
7753799	15507599	8	~1985
7754113	46524679	8	~1986
7754347	77543471	8	~1986
7754639	15509279	8	~1985
7754651	15509303	8	~1985
7754723	15509447	8	~1985
7754741	62037929	8	~1986
7754951	15509903	8	~1985
7754963	15509927	8	~1985
7755263	15510527	8	~1985

Exp.	Prime Factor	Digits	Year
7755653	46533919	8	~1986
7755793	46534759	8	~1986
7755851	15511703	8	~1985
7755889	186141337	9	~1987
7755959	15511919	8	~1985
7756157	62049257	8	~1986
7756321	46537927	8	~1986
7756633	46539799	8	~1986
7756633	170645927	9
7756781	62054249	8	~1986
7756951	77569511	8	~1986
7756961	62055689	8	~1986
7757041	46542247	8	~1986
7757551	558543673	9	~1989
7757699	15515399	8	~1985
7758083	15516167	8	~1985
7758329	62066633	8	~1986
7758743	15517487	8	~1985
7758769	170692919	9	~1987
7758899	62071193	8	~1986
7758911	15517823	8	~1985
7759099	186218377	9	~1987
7759151	15518303	8	~1985
7759513	46557079	8	~1986
7759777	46558663	8	~1986

4.724.182 digits

25-04-13