Small Mersenne Prime Factors (page 848/5025)

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
7305383	14610767	8	~1985
7305757	43834543	8	~1986
7305923	14611847	8	~1985
7306217	58449737	8	~1986
7306841	58454729	8	~1986
7307387	58459097	8	~1986
7307477	43844863	8	~1986
7307483	14614967	8	~1985
7307551	73075511	8	~1986
7307621	43845727	8	~1986
7307849	102309887	9	~1987
7308307	175399369	9	~1987
7308401	350803249	9	~1988
7308611	14617223	8	~1985
7308683	14617367	8	~1985
7309187	58473497	8	~1986
7309321	160805063	9	~1987
7309391	14618783	8	~1985
7309529	58476233	8	~1986
7309619	14619239	8	~1985
7309619	58476953	8
7309697	43858183	8	~1986
7309811	14619623	8	~1985
7310351	14620703	8	~1985
7310411	58483289	8	~1986

Exp.	Prime Factor	Digits	Year
7310579	175453897	9	~1987
7310843	14621687	8	~1985
7311011	233952353	9	~1988
7311047	58488377	8	~1986
7311119	14622239	8	~1985
7311209	102356927	9	~1987
7311347	58490777	8	~1986
7311431	14622863	8	~1985
7311593	43869559	8	~1986
7311659	14623319	8	~1985
7311737	43870423	8	~1986
7311779	131612023	9	~1987
7312013	43872079	8	~1986
7312139	14624279	8	~1985
7312493	43874959	8	~1986
7312517	43875103	8	~1986
7312961	58503689	8	~1986
7312979	14625959	8	~1985
7313291	14626583	8	~1985
7313567	58508537	8	~1986
7313693	43882159	8	~1986
7313729	58509833	8	~1986
7313881	117022097	9	~1987
7313903	14627807	8	~1985
7313951	14627903	8	~1985

Exp.	Prime Factor	Digits	Year
7314143	14628287	8	~1985
7314193	43885159	8	~1986
7314533	43887199	8	~1986
7314803	14629607	8	~1985
7314953	43889719	8	~1986
7315379	58523033	8	~1986
7315463	14630927	8	~1985
7315619	58524953	8	~1986
7315811	14631623	8	~1985
7316371	131694679	9	~1987
7316509	160963199	9	~1987
7316557	43899343	8	~1986
7316587	73165871	8	~1986
7316741	43900447	8	~1986
7316801	58534409	8	~1986
7316849	1975549231	10	~1990
7316909	58535273	8	~1986
7317041	58536329	8	~1986
7317043	307315807	9	~1988
7317119	14634239	8	~1985
7317143	14634287	8	~1985
7317553	43905319	8	~1986
7317731	14635463	8	~1985
7317851	14635703	8	~1985
7318037	43908223	8	~1986

Exp.	Prime Factor	Digits	Year
7318247	409821833	9	~1988
7318453	43910719	8	~1986
7318631	14637263	8	~1985
7318931	14637863	8	~1985
7318967	190293143	9	~1987
7319201	58553609	8	~1986
7319219	14638439	8	~1985
7319243	14638487	8	~1985
7319387	58555097	8	~1986
7319597	58556777	8	~1986
7319633	43917799	8	~1986
7319891	14639783	8	~1985
7319891	58559129	8
7320011	14640023	8	~1985
7320077	43920463	8	~1986
7320101	58560809	8	~1986
7320169	161043719	9	~1987
7320883	73208831	8	~1986
7320959	14641919	8	~1985
7320961	43925767	8	~1986
7320997	43925983	8	~1986
7321031	14642063	8	~1985
7321063	307484647	9	~1988
7321091	14642183	8	~1985
7321147	73211471	8	~1986

4.724.182 digits

25-04-13