Small Mersenne Prime Factors (page 291/5025)

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
1310579	2621159	7	~1979
1310723	2621447	7	~1979
1311097	31466329	8	~1981
1311143	2622287	7	~1979
1311239	2622479	7	~1979
1311287	10490297	8	~1980
1311311	2622623	7	~1979
1311433	60325919	8	~1982
1311503	31476073	8	~1981
1311509	18361127	8	~1981
1311523	52460921	8	~1982
1311617	49841447	8	~1982
1311623	94436857	8	~1983
1311797	10494377	8	~1980
1311923	2623847	7	~1979
1311971	10495769	8	~1980
1312027	62977297	8	~1982
1312093	7872559	7	~1980
1312183	31492393	8	~1981
1312301	10498409	8	~1980
1312319	2624639	7	~1979
1312319	31495657	8
1312331	2624663	7	~1979
1312343	41994977	8	~1982
1312379	2624759	7	~1979

Exp.	Prime Factor	Digits	Year
1312379	10499033	8
1312393	7874359	7	~1980
1312411	23623399	8	~1981
1312523	34125599	8	~1981
1312543	55126807	8	~1982
1312547	181131487	9	~1983
1312769	42008609	8	~1982
1312777	7876663	7	~1980
1312823	31507753	8	~1981
1312841	7877047	7	~1980
1312877	18380279	8	~1981
1312891	21006257	8	~1981
1312921	21006737	8	~1981
1312931	23632759	8	~1981
1312937	31510489	8	~1981
1313161	60405407	8	~1982
1313239	13132391	8	~1980
1313297	7879783	7	~1980
1313311	13133111	8	~1980
1313329	52533161	8	~1982
1313357	7880143	7	~1980
1313363	2626727	7	~1979
1313363	42027617	8
1313467	31523209	8	~1981
1313579	10508633	8	~1980

Exp.	Prime Factor	Digits	Year
1313629	115599353	9	~1983
1313699	2627399	7	~1979
1313813	7882879	7	~1980
1313959	13139591	8	~1980
1314101	10512809	8	~1980
1314127	44680319	8	~1982
1314179	2628359	7	~1979
1314191	2628383	7	~1979
1314239	42055649	8	~1982
1314497	10515977	8	~1980
1314539	42065249	8	~1982
1314563	2629127	7	~1979
1314823	55222567	8	~1982
1314851	2629703	7	~1979
1314851	63112849	8
1315211	2630423	7	~1979
1315213	21043409	8	~1981
1315231	23674159	8	~1981
1315367	31568809	8	~1981
1315621	60518567	8	~1982
1315673	7894039	7	~1980
1315823	2631647	7	~1979
1315871	2631743	7	~1979
1315889	31581337	8	~1981
1315891	52635641	8	~1982

Exp.	Prime Factor	Digits	Year
1315943	2631887	7	~1979
1316039	2632079	7	~1979
1316177	7897063	7	~1980
1316279	23693023	8	~1981
1316363	2632727	7	~1979
1316363	136901753	9
1316593	21065489	8	~1981
1316603	2633207	7	~1979
1316621	126395617	9	~1983
1316639	23699503	8	~1981
1316677	39500311	8	~1982
1316699	2633399	7	~1979
1316729	42135329	8	~1982
1316801	7900807	7	~1980
1316831	2633663	7	~1979
1316923	13169231	8	~1980
1317013	7902079	7	~1980
1317059	2634119	7	~1979
1317059	10536473	8
1317131	2634263	7	~1979
1317301	7903807	7	~1980
1317317	31615609	8	~1981
1317359	10538873	8	~1980
1317377	7904263	7	~1980
1317419	2634839	7	~1979

4.724.182 digits

25-04-13