Small Mersenne Prime Factors (page 910/5205)

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
8088389	64707113	8	~1986
8088467	64707737	8	~1986
8088761	64710089	8	~1986
8089049	64712393	8	~1986
8089391	16178783	8	~1985
8089619	16179239	8	~1985
8089799	16179599	8	~1985
8090041	3478717631	10	~1991
8090141	48540847	8	~1986
8090267	64722137	8	~1986
8090279	16180559	8	~1985
8090651	16181303	8	~1985
8090711	16181423	8	~1985
8090843	16181687	8	~1985
8090993	113273903	9	~1987
8091119	16182239	8	~1985
8091431	16182863	8	~1985
8091431	64731449	8
8091491	16182983	8	~1985
8091617	64732937	8	~1986
8091679	145650223	9	~1987
8092109	64736873	8	~1986
8092657	194223769	9	~1988
8092661	64741289	8	~1986
8092811	16185623	8	~1985

Exp.	Prime Factor	Digits	Year
8092817	64742537	8	~1986
8092919	16185839	8	~1985
8092967	1116829447	10	~1989
8093303	16186607	8	~1985
8093551	80935511	8	~1987
8093699	16187399	8	~1985
8093711	145686799	9	~1987
8094017	64752137	8	~1986
8094061	48564367	8	~1986
8094257	64754057	8	~1986
8094341	48566047	8	~1986
8094491	16188983	8	~1985
8094563	16189127	8	~1985
8094929	259037729	9	~1988
8095063	1554252097	10	~1990
8095231	582856633	9	~1989
8095259	16190519	8	~1985
8095343	16190687	8	~1985
8095441	48572647	8	~1986
8095469	64763753	8	~1986
8096041	129536657	9	~1987
8096171	16192343	8	~1985
8096183	16192367	8	~1985
8096197	48577183	8	~1986
8096219	64769753	8	~1986

Exp.	Prime Factor	Digits	Year
8096381	48578287	8	~1986
8096533	48579199	8	~1986
8096999	16193999	8	~1985
8097077	64776617	8	~1986
8097143	16194287	8	~1985
8097161	48582967	8	~1986
8097361	48584167	8	~1986
8097581	48585487	8	~1986
8097637	242929111	9	~1988
8097697	48586183	8	~1986
8097941	48587647	8	~1986
8098091	64784729	8	~1986
8098253	113375543	9	~1987
8098367	64786937	8	~1986
8098537	242956111	9	~1988
8098619	16197239	8	~1985
8098897	48593383	8	~1986
8099141	64793129	8	~1986
8099219	599342207	9	~1989
8099363	16198727	8	~1985
8099387	210584063	9	~1988
8099419	80994191	8	~1987
8099537	48597223	8	~1986
8099603	16199207	8	~1985
8099771	16199543	8	~1985

Exp.	Prime Factor	Digits	Year
8100097	48600583	8	~1986
8100217	129603473	9	~1987
8100359	16200719	8	~1985
8100413	48602479	8	~1986
8100419	16200839	8	~1985
8100629	64805033	8	~1986
8100637	48603823	8	~1986
8100731	16201463	8	~1985
8100803	16201607	8	~1985
8101031	16202063	8	~1985
8101057	129616913	9	~1987
8101133	48606799	8	~1986
8101283	16202567	8	~1985
8101637	64813097	8	~1986
8101811	16203623	8	~1985
8102441	48614647	8	~1986
8102459	16204919	8	~1985
8102579	16205159	8	~1985
8102639	16205279	8	~1985
8102713	48616279	8	~1986
8102723	16205447	8	~1985
8103071	16206143	8	~1985
8103083	16206167	8	~1985
8103187	81031871	8	~1987
8103239	16206479	8	~1985

4.903.097 digits

25-07-08