Small Mersenne Prime Factors (page 297/5025)

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
1353607	13536071	8	~1981
1353613	8121679	7	~1980
1353641	8121847	7	~1980
1353701	8122207	7	~1980
1353881	8123287	7	~1980
1353893	8123359	7	~1980
1353983	2707967	7	~1979
1354037	8124223	7	~1980
1354181	8125087	7	~1980
1354231	13542311	8	~1981
1354303	13543031	8	~1981
1354321	8125927	7	~1980
1354343	32504233	8	~1981
1354361	487569961	9	~1984
1354393	29796647	8	~1981
1354481	8126887	7	~1980
1354499	2708999	7	~1979
1354583	2709167	7	~1979
1354901	10839209	8	~1980
1354943	2709887	7	~1979
1354943	35228519	8
1354949	10839593	8	~1980
1355071	56912983	8	~1982
1355219	2710439	7	~1979
1355243	35236319	8	~1982

Exp.	Prime Factor	Digits	Year
1355267	10842137	8	~1980
1355297	40658911	8	~1982
1355303	75896969	8	~1982
1355423	2710847	7	~1979
1355443	21687089	8	~1981
1355447	35241623	8	~1982
1355533	8133199	7	~1980
1355657	8133943	7	~1980
1355693	18979703	8	~1981
1355741	10845929	8	~1980
1355749	32537977	8	~1981
1355891	2711783	7	~1979
1355917	32542009	8	~1981
1355933	8135599	7	~1980
1355941	21695057	8	~1981
1355983	46103423	8	~1982
1356059	2712119	7	~1979
1356143	2712287	7	~1979
1356269	10850153	8	~1980
1356319	13563191	8	~1981
1356331	13563311	8	~1981
1356497	8138983	7	~1980
1356539	2713079	7	~1979
1356611	2713223	7	~1979
1356659	56979679	8	~1982

Exp.	Prime Factor	Digits	Year
1356709	29847599	8	~1981
1356713	18993983	8	~1981
1356713	43414817	8
1356737	10853897	8	~1980
1356857	8141143	7	~1980
1356899	67844951	8	~1982
1357001	40710031	8	~1982
1357043	2714087	7	~1979
1357193	8143159	7	~1980
1357351	21717617	8	~1981
1357351	24432319	8
1357537	8145223	7	~1980
1357547	24435847	8	~1981
1357619	10860953	8	~1980
1357673	40730191	8	~1982
1357673	141197993	9
1357781	171080407	9	~1983
1357823	35303399	8	~1982
1357919	165666119	9	~1983
1358039	2716079	7	~1979
1358039	10864313	8
1358047	130372513	9	~1983
1358111	2716223	7	~1979
1358153	40744591	8	~1982
1358213	8149279	7	~1980

Exp.	Prime Factor	Digits	Year
1358281	21732497	8	~1981
1358297	29868951031	11	~1989
1358333	76066649	8	~1982
1358369	10866953	8	~1980
1358411	2716823	7	~1979
1358417	8150503	7	~1980
1358477	10867817	8	~1980
1358477	73357759	8
1358729	19022207	8	~1981
1358783	2717567	7	~1979
1358881	8153287	7	~1980
1358891	2717783	7	~1979
1359077	19027079	8	~1981
1359161	8154967	7	~1980
1359209	10873673	8	~1980
1359209	19028927	8
1359307	13593071	8	~1981
1359361	8156167	7	~1980
1359521	84290303	8	~1983
1359647	35350823	8	~1982
1359857	8159143	7	~1980
1359971	2719943	7	~1979
1360069	40802071	8	~1982
1360223	2720447	7	~1979
1360279	32646697	8	~1982

4.724.182 digits

25-04-13