Small Mersenne Prime Factors (page 690/5025)

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
5159663	10319327	8	~1983
5159669	72235367	8	~1985
5159677	30958063	8	~1985
5159711	10319423	8	~1983
5160329	72244607	8	~1985
5160377	30962263	8	~1985
5160413	30962479	8	~1985
5160613	30963679	8	~1985
5160719	10321439	8	~1983
5160791	10321583	8	~1983
5160803	10321607	8	~1983
5160839	10321679	8	~1983
5160923	10321847	8	~1983
5160959	10321919	8	~1983
5161357	82581713	8	~1986
5161411	51614111	8	~1985
5161451	41291609	8	~1985
5161529	371630089	9	~1987
5161571	10323143	8	~1983
5161921	30971527	8	~1985
5161997	567819671	9	~1988
5162123	10324247	8	~1983
5162177	278757559	9	~1987
5162587	1579751623	10	~1989
5162711	10325423	8	~1983

Exp.	Prime Factor	Digits	Year
5162831	10325663	8	~1983
5163377	30980263	8	~1985
5163517	30981103	8	~1985
5163751	51637511	8	~1985
5163883	51638831	8	~1985
5164123	51641231	8	~1985
5164331	10328663	8	~1983
5164361	30986167	8	~1985
5164591	51645911	8	~1985
5164609	247901233	9	~1987
5164897	30989383	8	~1985
5165113	30990679	8	~1985
5165123	10330247	8	~1983
5165423	10330847	8	~1983
5165519	10331039	8	~1983
5165591	10331183	8	~1983
5165647	51656471	8	~1985
5165687	712864807	9	~1988
5165833	743879953	9	~1988
5165939	10331879	8	~1983
5165947	206637881	9	~1987
5166061	30996367	8	~1985
5166101	30996607	8	~1985
5166131	10332263	8	~1983
5166179	41329433	8	~1985

Exp.	Prime Factor	Digits	Year
5166323	340977319	9	~1987
5166383	10332767	8	~1983
5166391	92995039	8	~1986
5166527	41332217	8	~1985
5166541	30999247	8	~1985
5167081	31002487	8	~1985
5167163	10334327	8	~1983
5167213	155016391	9	~1986
5167367	41338937	8	~1985
5167471	217033783	9	~1987
5167741	113690303	9	~1986
5167907	41343257	8	~1985
5167937	31007623	8	~1985
5168129	41345033	8	~1985
5168147	41345177	8	~1985
5168377	620205241	9	~1988
5168389	1602200591	10	~1989
5168623	82697969	8	~1986
5168711	10337423	8	~1983
5168837	31013023	8	~1985
5168869	155066071	9	~1986
5169023	341155519	9	~1987
5169137	41353097	8	~1985
5169299	10338599	8	~1983
5169401	31016407	8	~1985

Exp.	Prime Factor	Digits	Year
5169793	124075033	9	~1986
5169833	124075993	9	~1986
5169907	51699071	8	~1985
5169961	31019767	8	~1985
5170001	31020007	8	~1985
5170181	31021087	8	~1985
5170271	10340543	8	~1983
5170283	10340567	8	~1983
5170283	124086793	9
5170463	10340927	8	~1983
5170519	51705191	8	~1985
5170577	72388079	8	~1985
5170673	165461537	9	~1986
5170727	93073087	8	~1986
5170751	10341503	8	~1983
5171123	382663103	9	~1987
5171129	124107097	9	~1986
5171279	41370233	8	~1985
5171381	41371049	8	~1985
5171461	82743377	8	~1986
5171753	72404543	8	~1985
5171801	31030807	8	~1985
5171839	124124137	9	~1986
5171843	10343687	8	~1983
5171951	10343903	8	~1983

4.724.182 digits

25-04-13