Small Mersenne Prime Factors (page 249/5190)

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
1021799	2043599	7	~1978
1022129	63371999	8	~1982
1022167	10221671	8	~1980
1022179	18399223	8	~1980
1022243	2044487	7	~1978
1022629	24543097	8	~1981
1022653	6135919	7	~1979
1022653	22498367	8
1022849	8182793	7	~1979
1022899	10228991	8	~1980
1022977	30689311	8	~1981
1022977	177997999	9
1023047	92074231	8	~1982
1023277	6139663	7	~1979
1023301	6139807	7	~1979
1023367	18420607	8	~1980
1023461	6140767	7	~1979
1023551	8188409	7	~1979
1023577	6141463	7	~1979
1023653	14331143	8	~1980
1023719	2047439	7	~1978
1023821	32762273	8	~1981
1024031	2048063	7	~1978
1024087	10240871	8	~1980
1024171	16386737	8	~1980

Exp.	Prime Factor	Digits	Year
1024319	2048639	7	~1978
1024321	6145927	7	~1979
1024399	24585577	8	~1981
1024559	2049119	7	~1978
1024697	8197577	7	~1979
1024703	2049407	7	~1978
1024823	2049647	7	~1978
1024931	2049863	7	~1978
1024939	10249391	8	~1980
1025021	6150127	7	~1979
1025039	2050079	7	~1978
1025147	147621169	9	~1982
1025161	30754831	8	~1981
1025209	49210033	8	~1981
1025257	6151543	7	~1979
1025443	41017721	8	~1981
1025477	6152863	7	~1979
1025513	14357183	8	~1980
1025543	2051087	7	~1978
1025653	6153919	7	~1979
1025707	295403617	9	~1983
1025897	24621529	8	~1981
1026043	24625033	8	~1981
1026119	24626857	8	~1981
1026143	67725439	8	~1982

Exp.	Prime Factor	Digits	Year
1026217	71835191	8	~1982
1026251	2052503	7	~1978
1026401	6158407	7	~1979
1026427	10264271	8	~1980
1026457	16423313	8	~1980
1026479	2052959	7	~1978
1026563	2053127	7	~1978
1026581	63648023	8	~1982
1026593	88286999	8	~1982
1026677	8213417	7	~1979
1026679	10266791	8	~1980
1026791	18482239	8	~1980
1026799	10267991	8	~1980
1026859	24644617	8	~1981
1026913	6161479	7	~1979
1026947	57509033	8	~1981
1027031	49297489	8	~1981
1027097	8216777	7	~1979
1027211	180789137	9	~1983
1027319	2054639	7	~1978
1027417	49316017	8	~1981
1027471	43153783	8	~1981
1027547	57542633	8	~1981
1027591	49324369	8	~1981
1027693	6166159	7	~1979

Exp.	Prime Factor	Digits	Year
1027739	2055479	7	~1978
1027739	24665737	8
1027751	2055503	7	~1978
1027777	55499959	8	~1981
1027969	41118761	8	~1981
1028003	2056007	7	~1978
1028011	16448177	8	~1980
1028101	6168607	7	~1979
1028141	32900513	8	~1981
1028231	2056463	7	~1978
1028231	8225849	7
1028597	8228777	7	~1979
1028683	43204687	8	~1981
1028761	16460177	8	~1980
1028837	8230697	7	~1979
1028893	6173359	7	~1979
1028893	55560223	8
1028903	2057807	7	~1978
1028903	26751479	8
1028981	6173887	7	~1979
1028981	30869431	8
1028999	2057999	7	~1978
1029013	41160521	8	~1981
1029013	72030911	8
1029023	2058047	7	~1978

4.888.230 digits

25-06-29