Small Mersenne Prime Factors (page 711/5610)

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
5110871	40886969	8	~1985
5110883	10221767	8	~1983
5111131	214667503	9	~1987
5111231	10222463	8	~1983
5111261	40890089	8	~1985
5111299	122671177	9	~1986
5111303	10222607	8	~1983
5111317	235120583	9	~1987
5111651	10223303	8	~1983
5112001	30672007	8	~1985
5112059	10224119	8	~1983
5112067	245379217	9	~1987
5112119	40896953	8	~1985
5112181	603237359	9	~1988
5112361	30674167	8	~1985
5113037	153391111	9	~1986
5113211	10226423	8	~1983
5113331	10226663	8	~1983
5113343	10226687	8	~1983
5113769	40910153	8	~1985
5113783	51137831	8	~1985
5114327	40914617	8	~1985
5114357	40914857	8	~1985
5114419	245492113	9	~1987
5114471	10228943	8	~1983

Exp.	Prime Factor	Digits	Year
5114581	30687487	8	~1985
5114663	10229327	8	~1983
5114771	40918169	8	~1985
5114999	40919993	8	~1985
5115133	30690799	8	~1985
5115137	30690823	8	~1985
5115251	10230503	8	~1983
5115371	10230743	8	~1983
5115431	10230863	8	~1983
5115431	133001207	9
5115569	767335351	9	~1988
5115577	30693463	8	~1985
5115661	30693967	8	~1985
5115917	30695503	8	~1985
5116039	51160391	8	~1985
5116211	10232423	8	~1983
5116297	30697783	8	~1985
5116361	440007047	9	~1987
5116393	30698359	8	~1985
5116393	2077255559	10
5116537	30699223	8	~1985
5116607	92098927	8	~1986
5116691	10233383	8	~1983
5116897	30701383	8	~1985
5116981	30701887	8	~1985

Exp.	Prime Factor	Digits	Year
5117039	10234079	8	~1983
5117071	81873137	8	~1986
5117083	51170831	8	~1985
5117117	40936937	8	~1985
5117363	10234727	8	~1983
5117471	10234943	8	~1983
5117551	51175511	8	~1985
5117687	40941497	8	~1985
5118013	30708079	8	~1985
5118089	40944713	8	~1985
5118143	10236287	8	~1983
5118203	10236407	8	~1983
5118341	30710047	8	~1985
5118359	10236719	8	~1983
5118637	30711823	8	~1985
5119043	10238087	8	~1983
5119139	10238279	8	~1983
5119199	10238399	8	~1983
5119319	10238639	8	~1983
5119319	40954553	8
5119463	10238927	8	~1983
5119571	10239143	8	~1983
5119637	30717823	8	~1985
5119841	194553959	9	~1987
5119871	40958969	8	~1985

Exp.	Prime Factor	Digits	Year
5119909	112637999	9	~1986
5119973	30719839	8	~1985
5120263	51202631	8	~1985
5120371	81925937	8	~1986
5120597	276512239	9	~1987
5120657	30723943	8	~1985
5120831	10241663	8	~1983
5120957	40967657	8	~1985
5120957	71693399	8
5120963	10241927	8	~1983
5121209	40969673	8	~1985
5121323	10242647	8	~1983
5121353	30728119	8	~1985
5121359	10242719	8	~1983
5121667	81946673	8	~1986
5121821	30730927	8	~1985
5121841	30731047	8	~1985
5121911	10243823	8	~1983
5122121	30732727	8	~1985
5122277	71711879	8	~1985
5122433	71714063	8	~1985
5122679	10245359	8	~1983
5122739	10245479	8	~1983
5122889	71720447	8	~1985
5122919	10245839	8	~1983

5.307.017 digits

26-01-11