Small Mersenne Prime Factors (page 298/5730)

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
1301693	18223703	8	~1981
1301719	9229187711	10	~1987
1301779	13017791	8	~1980
1301851	75507359	8	~1982
1301879	2603759	7	~1979
1301893	7811359	7	~1980
1301939	2603879	7	~1979
1302017	10416137	8	~1980
1302293	7813759	7	~1980
1302373	7814239	7	~1980
1302373	28652207	8
1302443	2604887	7	~1979
1302443	33863519	8
1302461	7814767	7	~1980
1302827	10422617	8	~1980
1302839	93804409	8	~1983
1303091	2606183	7	~1979
1303283	125115169	9	~1983
1303327	31279849	8	~1981
1303363	44314343	8	~1982
1303453	7820719	7	~1980
1303453	28675967	8
1303499	2606999	7	~1979
1303633	59967119	8	~1982
1303711	13037111	8	~1980

Exp.	Prime Factor	Digits	Year
1303867	83447489	8	~1982
1303871	2607743	7	~1979
1303931	2607863	7	~1979
1303931	62588689	8
1304003	2608007	7	~1979
1304183	2608367	7	~1979
1304239	419964959	9	~1984
1304273	7825639	7	~1980
1304299	23477383	8	~1981
1304371	375658849	9	~1984
1304389	70437007	8	~1982
1304411	10435289	8	~1980
1304503	54789127	8	~1982
1304531	104362481	9	~1983
1304581	164377207	9	~1983
1304599	23482783	8	~1981
1304603	2609207	7	~1979
1304833	7828999	7	~1980
1304983	52199321	8	~1982
1305233	18273263	8	~1981
1305391	54826423	8	~1982
1305511	13055111	8	~1980
1305517	70497919	8	~1982
1305589	31334137	8	~1981
1305599	2611199	7	~1979

Exp.	Prime Factor	Digits	Year
1305607	242842903	9	~1984
1305637	31335289	8	~1981
1305653	18279143	8	~1981
1305659	10445273	8	~1980
1305739	23503303	8	~1981
1305743	2611487	7	~1979
1305743	54841207	8
1305803	41785697	8	~1982
1306087	31346089	8	~1981
1306223	96660503	8	~1983
1306273	7837639	7	~1980
1306439	2612879	7	~1979
1306489	39194671	8	~1982
1306499	2612999	7	~1979
1306517	7839103	7	~1980
1306601	10452809	8	~1980
1306691	10453529	8	~1980
1306751	2613503	7	~1979
1306831	54886903	8	~1982
1306889	10455113	8	~1980
1307051	2614103	7	~1979
1307069	39212071	8	~1982
1307087	62740177	8	~1982
1307093	73197209	8	~1982
1307101	7842607	7	~1980

Exp.	Prime Factor	Digits	Year
1307303	2614607	7	~1979
1307393	31377433	8	~1981
1307431	13074311	8	~1980
1307437	39223111	8	~1982
1307461	20919377	8	~1981
1307497	7844983	7	~1980
1307591	2615183	7	~1979
1307627	33998303	8	~1981
1307651	23537719	8	~1981
1307729	10461833	8	~1980
1307951	2615903	7	~1979
1308011	2616023	7	~1979
1308121	62789809	8	~1982
1308137	10465097	8	~1980
1308157	7848943	7	~1980
1308193	28780247	8	~1981
1308193	196228951	9
1308221	39246631	8	~1982
1308299	2616599	7	~1979
1308299	198861449	9
1308331	23549959	8	~1981
1308383	2616767	7	~1979
1308497	49722887	8	~1982
1308497	70658839	8
1308497	73275833	8

5.426.516 digits

26-03-08