Small Mersenne Prime Factors (page 442/5025)

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
2505127	45092287	8	~1983
2505143	5010287	7	~1981
2505143	60123433	8
2505253	40084049	8	~1983
2505337	496056727	9	~1986
2505353	35074943	8	~1983
2505361	55117943	8	~1983
2505383	60129193	8	~1984
2505499	325714871	9	~1985
2505527	125276351	9	~1984
2505541	15033247	8	~1982
2505793	60139033	8	~1984
2505847	25058471	8	~1983
2505857	60140569	8	~1984
2505901	15035407	8	~1982
2505983	5011967	7	~1981
2505991	25059911	8	~1983
2506033	15036199	8	~1982
2506079	5012159	7	~1981
2506129	55134839	8	~1983
2506277	15037663	8	~1982
2506279	45113023	8	~1983
2506373	15038239	8	~1982
2506619	45119143	8	~1983
2506657	15039943	8	~1982

Exp.	Prime Factor	Digits	Year
2506843	25068431	8	~1983
2506843	60164233	8
2506859	5013719	7	~1981
2507017	75210511	8	~1984
2507051	5014103	7	~1981
2507213	15043279	8	~1982
2507227	40115633	8	~1983
2507413	15044479	8	~1982
2507597	135410239	9	~1984
2507641	581772713	9	~1986
2507707	25077071	8	~1983
2507773	15046639	8	~1982
2507863	25078631	8	~1983
2507903	5015807	7	~1981
2508073	55177607	8	~1983
2508167	20065337	8	~1982
2508277	75248311	8	~1984
2508293	15049759	8	~1982
2508383	65217959	8	~1984
2508433	55185527	8	~1983
2508557	20068457	8	~1982
2508581	75257431	8	~1984
2508743	5017487	7	~1981
2509079	45163423	8	~1983
2509103	5018207	7	~1981

Exp.	Prime Factor	Digits	Year
2509163	5018327	7	~1981
2509271	5018543	7	~1981
2509279	25092791	8	~1983
2509337	15056023	8	~1982
2509499	5018999	7	~1981
2509627	25096271	8	~1983
2509627	40154033	8
2509777	15058663	8	~1982
2509841	15059047	8	~1982
2509861	15059167	8	~1982
2509963	25099631	8	~1983
2509993	15059959	8	~1982
2510051	140562857	9	~1984
2510171	5020343	7	~1981
2510219	306246719	9	~1985
2510309	60247417	8	~1984
2510533	15063199	8	~1982
2510591	5021183	7	~1981
2510609	20084873	8	~1982
2510723	5021447	7	~1981
2510731	25107311	8	~1983
2510731	120515089	9
2510741	15064447	8	~1982
2510771	5021543	7	~1981
2510803	361555633	9	~1985

Exp.	Prime Factor	Digits	Year
2511017	95418647	8	~1984
2511083	5022167	7	~1981
2511133	557471527	9	~1986
2511167	20089337	8	~1982
2511407	20091257	8	~1982
2511521	15069127	8	~1982
2511779	5023559	7	~1981
2511851	5023703	7	~1981
2512019	5024039	7	~1981
2512063	25120631	8	~1983
2512117	15072703	8	~1982
2512283	5024567	7	~1981
2512297	60295129	8	~1984
2512303	85418303	8	~1984
2512343	5024687	7	~1981
2512403	5024807	7	~1981
2512513	15075079	8	~1982
2512739	5025479	7	~1981
2512813	15076879	8	~1982
2512843	60308233	8	~1984
2513039	20104313	8	~1982
2513039	562920737	9
2513051	5026103	7	~1981
2513083	100523321	9	~1984
2513461	296588399	9	~1985

4.724.182 digits

25-04-13