Small Mersenne Prime Factors (page 706/5130)

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
5300423	10600847	8	~1983
5300579	42404633	8	~1985
5300623	53006231	8	~1985
5300831	10601663	8	~1983
5300993	31805959	8	~1985
5301071	10602143	8	~1983
5301301	636156121	9	~1988
5301311	10602623	8	~1983
5301313	31807879	8	~1985
5301349	159040471	9	~1986
5301533	74221463	8	~1986
5301547	53015471	8	~1985
5302091	10604183	8	~1983
5302103	10604207	8	~1983
5302151	42417209	8	~1985
5302163	10604327	8	~1983
5302307	42418457	8	~1985
5302327	95441887	8	~1986
5302573	31815439	8	~1985
5302763	10605527	8	~1983
5302987	84847793	8	~1986
5302991	10605983	8	~1983
5303003	10606007	8	~1983
5303141	31818847	8	~1985
5303183	10606367	8	~1983

Exp.	Prime Factor	Digits	Year
5303213	169702817	9	~1986
5303327	127279849	9	~1986
5303579	10607159	8	~1983
5303651	42429209	8	~1985
5303659	53036591	8	~1985
5303807	42430457	8	~1985
5303819	551597177	9	~1988
5303891	10607783	8	~1983
5303951	10607903	8	~1983
5304001	31824007	8	~1985
5304083	10608167	8	~1983
5304241	31825447	8	~1985
5304367	53043671	8	~1985
5304371	10608743	8	~1983
5304371	42434969	8
5304571	84873137	8	~1986
5304581	42436649	8	~1985
5304839	42438713	8	~1985
5305033	31830199	8	~1985
5305151	137933927	9	~1986
5305451	10610903	8	~1983
5305481	31832887	8	~1985
5305697	42445577	8	~1985
5305747	53057471	8	~1985
5305799	10611599	8	~1983

Exp.	Prime Factor	Digits	Year
5306531	10613063	8	~1983
5306627	42453017	8	~1985
5306783	10613567	8	~1983
5306963	10613927	8	~1983
5307073	31842439	8	~1985
5307083	10614167	8	~1983
5307509	42460073	8	~1985
5307563	10615127	8	~1983
5307719	10615439	8	~1983
5307781	31846687	8	~1985
5307803	10615607	8	~1983
5308333	31849999	8	~1985
5308379	10616759	8	~1983
5308441	31850647	8	~1985
5308451	42467609	8	~1985
5308577	42468617	8	~1985
5308679	127408297	9	~1986
5308789	116793359	9	~1986
5309053	286688863	9	~1987
5309123	10618247	8	~1983
5309663	10619327	8	~1983
5309713	31858279	8	~1985
5309891	10619783	8	~1983
5309963	10619927	8	~1983
5310157	31860943	8	~1985

Exp.	Prime Factor	Digits	Year
5310293	31861759	8	~1985
5310379	127449097	9	~1986
5310439	53104391	8	~1985
5310559	95590063	8	~1986
5310743	10621487	8	~1983
5310841	31865047	8	~1985
5310863	10621727	8	~1983
5310911	10621823	8	~1983
5310983	10621967	8	~1983
5311139	10622279	8	~1983
5311277	31867663	8	~1985
5311441	31868647	8	~1985
5311441	84983057	8
5311511	10623023	8	~1983
5311547	42492377	8	~1985
5311567	308070887	9	~1987
5311589	42492713	8	~1985
5311703	10623407	8	~1983
5311951	53119511	8	~1985
5312159	10624319	8	~1983
5312171	10624343	8	~1983
5312171	42497369	8
5312207	42497657	8	~1985
5312207	127492969	9
5312323	84997169	8	~1986

4.828.532 digits

25-06-01