Small Mersenne Prime Factors (page 499/5745)

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
2863967	68735209	8	~1984
2863979	51551623	8	~1984
2864051	5728103	7	~1981
2864083	97378823	8	~1984
2864159	5728319	7	~1981
2864221	17185327	8	~1983
2864357	40100999	8	~1984
2864363	5728727	7	~1981
2864371	28643711	8	~1983
2864453	40102343	8	~1984
2864633	85938991	8	~1984
2864671	28646711	8	~1983
2864713	17188279	8	~1983
2864723	5729447	7	~1981
2864909	40108727	8	~1984
2865001	45840017	8	~1984
2865007	68760169	8	~1984
2865091	28650911	8	~1983
2865329	22922633	8	~1983
2865431	5730863	7	~1981
2865491	5730983	7	~1981
2865497	22923977	8	~1983
2865497	40116959	8
2865521	91696673	8	~1984
2865743	5731487	7	~1981

Exp.	Prime Factor	Digits	Year
2865839	5731679	7	~1981
2865899	5731799	7	~1981
2865931	137564689	9	~1985
2865953	17195719	8	~1983
2866147	45858353	8	~1984
2866309	63058799	8	~1984
2866333	68791993	8	~1984
2866363	28663631	8	~1983
2866499	5732999	7	~1981
2866811	229344881	9	~1985
2866883	68805193	8	~1984
2866943	5733887	7	~1981
2867003	212158223	9	~1985
2867107	114684281	9	~1985
2867213	40140983	8	~1984
2867213	68813113	8
2867219	5734439	7	~1981
2867239	51610303	8	~1984
2867243	74548319	8	~1984
2867269	68814457	8	~1984
2867281	17203687	8	~1983
2867297	17203783	8	~1983
2867297	40142159	8
2867303	5734607	7	~1981
2867471	5734943	7	~1981

Exp.	Prime Factor	Digits	Year
2867561	17205367	8	~1983
2867699	51618583	8	~1984
2867807	22942457	8	~1983
2867857	17207143	8	~1983
2867873	68828953	8	~1984
2867933	40151063	8	~1984
2868083	5736167	7	~1981
2868137	68835289	8	~1984
2868161	17208967	8	~1983
2868191	51627439	8	~1984
2868251	5736503	7	~1981
2868263	5736527	7	~1981
2868331	45893297	8	~1984
2868451	28684511	8	~1983
2868479	68843497	8	~1984
2868617	40160639	8	~1984
2868713	315558431	9	~1986
2868779	5737559	7	~1981
2868851	5737703	7	~1981
2868857	17213143	8	~1983
2868871	28688711	8	~1983
2869001	17214007	8	~1983
2869001	137712049	9
2869051	803334281	9	~1987
2869103	5738207	7	~1981

Exp.	Prime Factor	Digits	Year
2869253	17215519	8	~1983
2869327	28693271	8	~1983
2869441	63127703	8	~1984
2869459	120517279	9	~1985
2869547	22956377	8	~1983
2869553	86086591	8	~1984
2869567	51652207	8	~1984
2869793	17218759	8	~1983
2869859	68876617	8	~1984
2869943	5739887	7	~1981
2870017	17220103	8	~1983
2870039	5740079	7	~1981
2870051	5740103	7	~1981
2870081	17220487	8	~1983
2870099	51661783	8	~1984
2870183	5740367	7	~1981
2870473	63150407	8	~1984
2870513	17223079	8	~1983
2870513	40187183	8
2870519	5741039	7	~1981
2870531	5741063	7	~1981
2870573	17223439	8	~1983
2870591	22964729	8	~1983
2870627	51671287	8	~1984
2870627	143531351	9

5.441.361 digits

26-03-15