Small Mersenne Prime Factors (page 475/5025)

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
2808061	16848367	8	~1982
2808269	39315767	8	~1983
2808347	22466777	8	~1983
2808359	5616719	7	~1981
2808433	16850599	8	~1982
2808521	16851127	8	~1982
2808583	44937329	8	~1984
2808593	89874977	8	~1984
2808977	39325679	8	~1983
2809007	22472057	8	~1983
2809091	5618183	7	~1981
2809091	22472729	8
2809349	39330887	8	~1983
2809451	5618903	7	~1981
2809507	28095071	8	~1983
2809553	67429273	8	~1984
2809643	5619287	7	~1981
2809973	16859839	8	~1982
2810051	5620103	7	~1981
2810077	44961233	8	~1984
2810161	16860967	8	~1982
2810191	44963057	8	~1984
2810359	67448617	8	~1984
2810371	28103711	8	~1983
2810399	5620799	7	~1981

Exp.	Prime Factor	Digits	Year
2810579	5621159	7	~1981
2810657	16863943	8	~1982
2810663	5621327	7	~1981
2810711	5621423	7	~1981
2811131	5622263	7	~1981
2811169	84335071	8	~1984
2811181	16867087	8	~1982
2811299	5622599	7	~1981
2811311	5622623	7	~1981
2811337	16868023	8	~1982
2811353	16868119	8	~1982
2811407	208044119	9	~1985
2811509	22492073	8	~1983
2811533	16869199	8	~1982
2811533	39361463	8
2811583	28115831	8	~1983
2811761	22494089	8	~1983
2811833	16870999	8	~1982
2811863	5623727	7	~1981
2811883	44990129	8	~1984
2811983	5623967	7	~1981
2812169	22497353	8	~1983
2812219	28122191	8	~1983
2812223	5624447	7	~1981
2812297	16873783	8	~1982

Exp.	Prime Factor	Digits	Year
2812307	73119983	8	~1984
2812331	22498649	8	~1983
2812343	5624687	7	~1981
2812619	5625239	7	~1981
2812639	28126391	8	~1983
2812801	61881623	8	~1984
2812811	22502489	8	~1983
2812813	16876879	8	~1982
2812897	16877383	8	~1982
2812937	84388111	8	~1984
2813039	5626079	7	~1981
2813171	5626343	7	~1981
2813183	5626367	7	~1981
2813257	557024887	9	~1986
2813353	16880119	8	~1982
2813411	50641399	8	~1984
2813563	45017009	8	~1984
2813663	5627327	7	~1981
2813663	478322711	9
2813711	5627423	7	~1981
2813737	16882423	8	~1982
2813851	28138511	8	~1983
2814041	90049313	8	~1984
2814089	22512713	8	~1983
2814419	5628839	7	~1981

Exp.	Prime Factor	Digits	Year
2814431	5628863	7	~1981
2814557	219535447	9	~1985
2814599	5629199	7	~1981
2814817	16888903	8	~1982
2814863	5629727	7	~1981
2814881	16889287	8	~1982
2814991	28149911	8	~1983
2815049	39410687	8	~1983
2815187	22521497	8	~1983
2815271	22522169	8	~1983
2815313	39414383	8	~1983
2815331	5630663	7	~1981
2815331	22522649	8
2815691	5631383	7	~1981
2815877	242165423	9	~1985
2815973	16895839	8	~1983
2816239	28162391	8	~1983
2816269	61957919	8	~1984
2816399	5632799	7	~1981
2816399	22531193	8
2816459	5632919	7	~1981
2816519	5633039	7	~1981
2816633	39432863	8	~1983
2816701	16900207	8	~1983
2816899	28168991	8	~1983

4.724.182 digits

25-04-13