Small Mersenne Prime Factors (page 618/5790)

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
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
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

Exp.	Prime Factor	Digits	Year
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
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

Exp.	Prime Factor	Digits	Year
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
4014293	56200103	8	~1985
4014313	24085879	8	~1984
4014403	40144031	8	~1984
4014559	72262063	8	~1985
4014617	96350809	8	~1985
4014739	40147391	8	~1984
4014821	152563199	9	~1986
4014887	32119097	8	~1984
4014971	8029943	7	~1983
4015283	8030567	7	~1983
4015307	32122457	8	~1984
4015331	8030663	7	~1983
4015463	8030927	7	~1983
4015559	8031119	7	~1983
4015577	56218079	8	~1985
4015637	56218919	8	~1985

Exp.	Prime Factor	Digits	Year
4015679	32125433	8	~1984
4015811	168664063	9	~1986
4015883	8031767	7	~1983
4015981	24095887	8	~1984
4016161	24096967	8	~1984
4016219	8032439	7	~1983
4016477	24098863	8	~1984
4016561	32132489	8	~1984
4016741	32133929	8	~1984
4016773	24100639	8	~1984
4016863	40168631	8	~1984
4017007	40170071	8	~1984
4017007	64272113	8
4017131	8034263	7	~1983
4017313	64277009	8	~1985
4017547	136596599	9	~1986
4017599	32140793	8	~1984
4017731	8035463	7	~1983
4017803	8035607	7	~1983
4017931	64286897	8	~1985
4018081	313410319	9	~1986
4018087	40180871	8	~1984
4018087	96434089	8
4018207	64291313	8	~1985
4018627	40186271	8	~1984

5.486.313 digits

26-04-05