Small Mersenne Prime Factors (page 713/5670)

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
5106317	30637903	8	~1985
5106559	245114833	9	~1987
5106719	10213439	8	~1983
5106823	81709169	8	~1986
5107139	10214279	8	~1983
5107331	10214663	8	~1983
5107379	40859033	8	~1985
5107379	91932823	8
5107439	40859513	8	~1985
5107481	194084279	9	~1987
5107643	10215287	8	~1983
5107651	91937719	8	~1986
5107691	10215383	8	~1983
5107693	30646159	8	~1985
5107709	71507927	8	~1985
5107801	30646807	8	~1985
5107997	71511959	8	~1985
5108039	10216079	8	~1983
5108137	30648823	8	~1985
5108399	10216799	8	~1983
5108569	112388519	9	~1986
5108581	204343241	9	~1987
5108639	10217279	8	~1983
5108639	40869113	8
5108639	91955503	8

Exp.	Prime Factor	Digits	Year
5109037	30654223	8	~1985
5109113	71527583	8	~1985
5109173	30655039	8	~1985
5109179	10218359	8	~1983
5109491	91970839	8	~1986
5109551	10219103	8	~1983
5109617	40876937	8	~1985
5109961	30659767	8	~1985
5110211	40881689	8	~1985
5110223	10220447	8	~1983
5110289	40882313	8	~1985
5110361	30662167	8	~1985
5110541	40884329	8	~1985
5110709	153321271	9	~1986
5110717	30664303	8	~1985
5110769	71550767	8	~1985
5110811	10221623	8	~1983
5110823	10221647	8	~1983
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

Exp.	Prime Factor	Digits	Year
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
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

Exp.	Prime Factor	Digits	Year
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
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

5.366.787 digits

26-02-08