Small Mersenne Prime Factors (page 405/5025)

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
2185871	4371743	7	~1980
2186003	4372007	7	~1980
2186011	34976177	8	~1983
2186227	52469449	8	~1983
2186537	52476889	8	~1983
2186543	4373087	7	~1980
2186579	17492633	8	~1982
2186603	4373207	7	~1980
2186689	52480537	8	~1983
2187049	104978353	9	~1984
2187061	48115343	8	~1983
2187193	34995089	8	~1983
2187511	39375199	8	~1983
2187683	4375367	7	~1980
2187743	4375487	7	~1980
2187811	21878111	8	~1982
2187877	13127263	8	~1982
2187953	490101473	9	~1986
2187961	35007377	8	~1983
2187973	13127839	8	~1982
2188031	4376063	7	~1980
2188049	83145863	8	~1984
2188157	30634199	8	~1983
2188271	266969063	9	~1985
2188279	39389023	8	~1983

Exp.	Prime Factor	Digits	Year
2188331	4376663	7	~1980
2188411	21884111	8	~1982
2188531	35016497	8	~1983
2188583	4377167	7	~1980
2188609	48149399	8	~1983
2188679	70037729	8	~1983
2188691	91925023	8	~1984
2188799	4377599	7	~1980
2188877	30644279	8	~1983
2188919	4377839	7	~1980
2188919	17511353	8
2189017	65670511	8	~1983
2189081	13134487	8	~1982
2189171	17513369	8	~1982
2189281	13135687	8	~1982
2189533	48169727	8	~1983
2189639	4379279	7	~1980
2189699	4379399	7	~1980
2189723	4379447	7	~1980
2189743	52553833	8	~1983
2189783	4379567	7	~1980
2189879	4379759	7	~1980
2189881	35038097	8	~1983
2190077	17520617	8	~1982
2190131	4380263	7	~1980

Exp.	Prime Factor	Digits	Year
2190143	4380287	7	~1980
2190173	486218407	9	~1985
2190193	13141159	8	~1982
2190217	35043473	8	~1983
2190299	4380599	7	~1980
2190347	17522777	8	~1982
2190403	35046449	8	~1983
2190541	48191903	8	~1983
2190737	83248007	8	~1984
2190857	17526857	8	~1982
2190983	4381967	7	~1980
2190983	52583593	8
2191171	39441079	8	~1983
2191331	4382663	7	~1980
2191711	39450799	8	~1983
2191883	4383767	7	~1980
2192051	4384103	7	~1980
2192053	48225167	8	~1983
2192059	39457063	8	~1983
2192089	48225959	8	~1983
2192131	35074097	8	~1983
2192143	35074289	8	~1983
2192257	35076113	8	~1983
2192261	17538089	8	~1982
2192363	4384727	7	~1980

Exp.	Prime Factor	Digits	Year
2192423	4384847	7	~1980
2192471	4384943	7	~1980
2192579	4385159	7	~1980
2192629	52623097	8	~1983
2192791	21927911	8	~1982
2192791	35084657	8
2192837	17542697	8	~1982
2192917	52630009	8	~1983
2192941	13157647	8	~1982
2193097	65792911	8	~1983
2193097	521957087	9
2193167	17545337	8	~1982
2193239	39478303	8	~1983
2193239	52637737	8
2193311	4386623	7	~1980
2193311	17546489	8
2193313	13159879	8	~1982
2193413	13160479	8	~1982
2193421	157926313	9	~1984
2193469	140382017	9	~1984
2193547	21935471	8	~1982
2193641	65809231	8	~1983
2193673	35098769	8	~1983
2193689	17549513	8	~1982
2193707	57036383	8	~1983

4.724.182 digits

25-04-13