Small Mersenne Prime Factors (page 614/5670)

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
4005791	8011583	7	~1983
4005983	8011967	7	~1983
4006019	32048153	8	~1984
4006097	32048777	8	~1984
4006259	8012519	7	~1983
4006319	8012639	7	~1983
4006349	96152377	8	~1985
4006351	64101617	8	~1985
4006417	24038503	8	~1984
4006567	64105073	8	~1985
4006721	24040327	8	~1984
4006811	8013623	7	~1983
4007039	8014079	7	~1983
4007099	8014199	7	~1983
4007123	8014247	7	~1983
4007219	72129943	8	~1985
4007351	8014703	7	~1983
4007429	56104007	8	~1985
4007477	32059817	8	~1984
4007477	56104679	8
4007519	8015039	7	~1983
4007551	64120817	8	~1985
4007599	40075991	8	~1984
4007741	32061929	8	~1984
4007963	8015927	7	~1983

Exp.	Prime Factor	Digits	Year
4008001	24048007	8	~1984
4008143	8016287	7	~1983
4008149	96195577	8	~1985
4008239	8016479	7	~1983
4008421	24050527	8	~1984
4008559	72154063	8	~1985
4008671	8017343	7	~1983
4008713	56121983	8	~1985
4008841	24053047	8	~1984
4008853	24053119	8	~1984
4008997	24053983	8	~1984
4008997	64143953	8
4009037	56126519	8	~1985
4009091	8018183	7	~1983
4009139	8018279	7	~1983
4009139	72164503	8
4009151	8018303	7	~1983
4009319	8018639	7	~1983
4009319	72167743	8
4009391	8018783	7	~1983
4009391	32075129	8
4009417	24056503	8	~1984
4009639	72173503	8	~1985
4009823	8019647	7	~1983
4009897	24059383	8	~1984

Exp.	Prime Factor	Digits	Year
4009919	8019839	7	~1983
4009939	40099391	8	~1984
4009991	8019983	7	~1983
4010131	40101311	8	~1984
4010231	104266007	9	~1985
4010353	64165649	8	~1985
4010353	1146960959	10
4010647	40106471	8	~1984
4010663	8021327	7	~1983
4010819	8021639	7	~1983
4010857	24065143	8	~1984
4010857	64173713	8
4010893	24065359	8	~1984
4011053	24066319	8	~1984
4011103	96266473	8	~1985
4011257	32090057	8	~1984
4011263	8022527	7	~1983
4011347	72204247	8	~1985
4011377	24068263	8	~1984
4011647	96279529	8	~1985
4011653	56163143	8	~1985
4011871	72213679	8	~1985
4011929	32095433	8	~1984
4012013	24072079	8	~1984
4012037	32096297	8	~1984

Exp.	Prime Factor	Digits	Year
4012193	248755967	9	~1986
4012199	8024399	7	~1983
4012271	8024543	7	~1983
4012321	24073927	8	~1984
4012441	24074647	8	~1984
4012487	192599377	9	~1986
4012549	88276079	8	~1985
4012709	32101673	8	~1984
4012721	1187765417	10	~1988
4012829	32102633	8	~1984
4012847	104334023	9	~1985
4013111	8026223	7	~1983
4013153	56184143	8	~1985
4013363	8026727	7	~1983
4013567	96325609	8	~1985
4013591	72244639	8	~1985
4013621	24081727	8	~1984
4013651	8027303	7	~1983
4013897	24083383	8	~1984
4013993	56195903	8	~1985
4014011	32112089	8	~1984
4014011	72252199	8
4014203	8028407	7	~1983
4014229	88313039	8	~1985
4014239	8028479	7	~1983

5.366.787 digits

26-02-08