Small Mersenne Prime Factors (page 396/5025)

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
2109791	4219583	7	~1980
2109869	63296071	8	~1983
2109911	4219823	7	~1980
2109973	63299191	8	~1983
2110019	4220039	7	~1980
2110037	29540519	8	~1982
2110063	21100631	8	~1982
2110103	4220207	7	~1980
2110259	4220519	7	~1980
2110343	4220687	7	~1980
2110439	37987903	8	~1983
2110469	29546567	8	~1982
2110523	4221047	7	~1980
2110543	21105431	8	~1982
2110553	12663319	8	~1982
2110621	63318631	8	~1983
2111051	16888409	8	~1982
2111159	4222319	7	~1980
2111177	12667063	8	~1982
2111231	16889849	8	~1982
2111311	21113111	8	~1982
2111311	38003599	8
2111357	29558999	8	~1982
2111387	16891097	8	~1982
2111453	29560343	8	~1982

Exp.	Prime Factor	Digits	Year
2111491	21114911	8	~1982
2111497	12668983	8	~1982
2111513	12669079	8	~1982
2111579	50677897	8	~1983
2111771	4223543	7	~1980
2111789	67577249	8	~1983
2111897	12671383	8	~1982
2111897	50685529	8
2112017	202753633	9	~1984
2112161	12672967	8	~1982
2112191	4224383	7	~1980
2112329	16898633	8	~1982
2112337	12674023	8	~1982
2112353	50696473	8	~1983
2112353	168988241	9
2112419	4224839	7	~1980
2112569	16900553	8	~1982
2112713	67606817	8	~1983
2112827	16902617	8	~1982
2112827	50707849	8
2112841	46482503	8	~1983
2112953	12677719	8	~1982
2113037	12678223	8	~1982
2113211	4226423	7	~1980
2113451	4226903	7	~1980

Exp.	Prime Factor	Digits	Year
2113471	38042479	8	~1983
2113511	4227023	7	~1980
2113513	12681079	8	~1982
2113733	67639457	8	~1983
2113819	38048743	8	~1983
2113879	21138791	8	~1982
2113949	16911593	8	~1982
2114039	4228079	7	~1980
2114087	38053567	8	~1983
2114221	46512863	8	~1983
2114243	4228487	7	~1980
2114351	359439671	9	~1985
2114363	4228727	7	~1980
2114507	16916057	8	~1982
2114533	63435991	8	~1983
2114771	4229543	7	~1980
2114857	97283423	8	~1984
2114887	1053213727	10	~1986
2115059	4230119	7	~1980
2115077	12690463	8	~1982
2115229	46535039	8	~1983
2115493	12692959	8	~1982
2115499	84619961	8	~1984
2115671	16925369	8	~1982
2115677	12694063	8	~1982

Exp.	Prime Factor	Digits	Year
2115703	33851249	8	~1983
2115721	12694327	8	~1982
2115761	16926089	8	~1982
2115847	122719127	9	~1984
2115943	21159431	8	~1982
2115943	33855089	8
2115979	21159791	8	~1982
2115983	4231967	7	~1980
2116027	38088487	8	~1983
2116039	38088703	8	~1983
2116099	38089783	8	~1983
2116123	33857969	8	~1983
2116307	16930457	8	~1982
2116393	12698359	8	~1982
2116393	84655721	8
2116481	12698887	8	~1982
2116523	50796553	8	~1983
2116601	12699607	8	~1982
2116717	33867473	8	~1983
2116757	29634599	8	~1982
2116813	63504391	8	~1983
2116817	12700903	8	~1982
2116901	16935209	8	~1982
2117051	4234103	7	~1980
2117051	38106919	8

4.724.182 digits

25-04-13