Small Mersenne Prime Factors (page 938/5460)

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
8287871	66302969	8	~1986
8288057	66304457	8	~1986
8288081	314947079	9	~1988
8288183	16576367	8	~1985
8288353	49730119	8	~1986
8288459	16576919	8	~1985
8288543	16577087	8	~1985
8288587	82885871	8	~1987
8288681	49732087	8	~1986
8288977	49733863	8	~1986
8289023	16578047	8	~1985
8289101	66312809	8	~1986
8289383	16578767	8	~1985
8289419	16578839	8	~1985
8289581	49737487	8	~1986
8289587	66316697	8	~1986
8289647	66317177	8	~1986
8289731	16579463	8	~1985
8289767	66318137	8	~1986
8290043	16580087	8	~1985
8290043	198961033	9
8290151	16580303	8	~1985
8290319	16580639	8	~1985
8290427	66323417	8	~1986
8290559	16581119	8	~1985

Exp.	Prime Factor	Digits	Year
8290643	16581287	8	~1985
8290861	49745167	8	~1986
8290901	49745407	8	~1986
8290907	66327257	8	~1986
8291099	16582199	8	~1985
8291113	49746679	8	~1986
8291237	66329897	8	~1986
8291357	49748143	8	~1986
8291401	49748407	8	~1986
8291573	49749439	8	~1986
8291681	49750087	8	~1986
8291813	49750879	8	~1986
8292001	49752007	8	~1986
8292023	16584047	8	~1985
8292079	82920791	8	~1987
8292217	49753303	8	~1986
8292359	16584719	8	~1985
8292503	16585007	8	~1985
8292671	348292183	9	~1988
8292707	66341657	8	~1987
8292737	49756423	8	~1986
8292941	49757647	8	~1986
8293057	49758343	8	~1986
8293223	16586447	8	~1985
8293283	16586567	8	~1985

Exp.	Prime Factor	Digits	Year
8293511	66348089	8	~1987
8293619	16587239	8	~1985
8293829	447866767	9	~1989
8294171	16588343	8	~1985
8294183	16588367	8	~1985
8294339	16588679	8	~1985
8294411	16588823	8	~1985
8294437	49766623	8	~1986
8294483	16588967	8	~1985
8294543	16589087	8	~1985
8294617	49767703	8	~1986
8294729	116126207	9	~1987
8294879	16589759	8	~1985
8294999	16589999	8	~1985
8295137	1990832881	10	~1990
8295179	16590359	8	~1985
8295239	16590479	8	~1985
8295557	66364457	8	~1987
8295697	7018159663	10	~1991
8296199	16592399	8	~1985
8296259	16592519	8	~1985
8296333	49777999	8	~1986
8296397	49778383	8	~1986
8296439	16592879	8	~1985
8296649	116153087	9	~1987

Exp.	Prime Factor	Digits	Year
8296657	132746513	9	~1987
8296751	16593503	8	~1985
8296853	199124473	9	~1988
8296919	16593839	8	~1985
8297027	199128649	9	~1988
8297171	16594343	8	~1985
8297279	16594559	8	~1985
8297437	1045477063	10	~1989
8297519	16595039	8	~1985
8297537	66380297	8	~1987
8297789	66382313	8	~1987
8298071	16596143	8	~1985
8298289	199158937	9	~1988
8298539	16597079	8	~1985
8298847	82988471	8	~1987
8299169	116188367	9	~1987
8299259	66394073	8	~1987
8299931	66399449	8	~1987
8300057	66400457	8	~1987
8300393	49802359	8	~1986
8300753	265624097	9	~1988
8300801	66406409	8	~1987
8301179	16602359	8	~1985
8301463	132823409	9	~1987
8301877	49811263	8	~1986

5.157.210 digits

25-11-02