Small Mersenne Prime Factors (page 973/6105)

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
8280911	16561823	8	~1985
8281313	49687879	8	~1986
8281379	16562759	8	~1985
8281571	16563143	8	~1985
8281579	82815791	8	~1987
8282003	16564007	8	~1985
8282063	16564127	8	~1985
8282129	66257033	8	~1987
8282159	16564319	8	~1985
8282189	115950647	9	~1987
8282291	66258329	8	~1987
8282411	149083399	9	~1987
8282453	115954343	9	~1987
8282633	49695799	8	~1986
8282759	16565519	8	~1985
8283001	49698007	8	~1986
8283257	49699543	8	~1986
8283263	16566527	8	~1985
8283503	16567007	8	~1985
8283547	82835471	8	~1987
8283923	16567847	8	~1985
8284033	49704199	8	~1986
8284103	16568207	8	~1985
8284127	66273017	8	~1987
8284373	198824953	9	~1988

Exp.	Prime Factor	Digits	Year
8284447	82844471	8	~1987
8284739	16569479	8	~1985
8284823	16569647	8	~1985
8284823	198835753	9
8284841	49709047	8	~1986
8284949	66279593	8	~1987
8285411	16570823	8	~1985
8285591	16571183	8	~1985
8285621	66284969	8	~1987
8285639	66285113	8	~1987
8285831	16571663	8	~1985
8286203	16572407	8	~1985
8286209	66289673	8	~1987
8286253	49717519	8	~1986
8286569	513767279	9	~1989
8286671	16573343	8	~1985
8286683	16573367	8	~1985
8286731	16573463	8	~1985
8287271	16574543	8	~1985
8287717	132603473	9	~1987
8287817	49726903	8	~1986
8287871	66302969	8	~1987
8288057	66304457	8	~1987
8288081	314947079	9	~1988
8288183	16576367	8	~1985

Exp.	Prime Factor	Digits	Year
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	~1987
8289383	16578767	8	~1985
8289419	16578839	8	~1985
8289581	49737487	8	~1986
8289587	66316697	8	~1987
8289647	66317177	8	~1987
8289731	16579463	8	~1985
8289767	66318137	8	~1987
8290043	16580087	8	~1985
8290043	198961033	9
8290151	16580303	8	~1985
8290319	16580639	8	~1985
8290427	66323417	8	~1987
8290559	16581119	8	~1985
8290643	16581287	8	~1985
8290861	49745167	8	~1986
8290901	49745407	8	~1986
8290907	66327257	8	~1987

Exp.	Prime Factor	Digits	Year
8291099	16582199	8	~1985
8291113	49746679	8	~1986
8291237	66329897	8	~1987
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
8293511	66348089	8	~1987
8293619	16587239	8	~1985
8293829	447866767	9	~1989
8294171	16588343	8	~1985

5.800.574 digits

26-08-30