Small Mersenne Prime Factors (page 913/5205)

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
8135797	48814783	8	~1986
8136143	16272287	8	~1985
8136551	65092409	8	~1986
8136743	16273487	8	~1985
8137411	130198577	9	~1987
8137517	48825103	8	~1986
8137631	16275263	8	~1985
8137813	48826879	8	~1986
8138111	16276223	8	~1985
8138363	16276727	8	~1985
8138539	81385391	8	~1987
8138579	16277159	8	~1985
8138861	65110889	8	~1986
8138863	276721343	9	~1988
8139119	16278239	8	~1985
8139359	16278719	8	~1985
8139431	16278863	8	~1985
8139553	48837319	8	~1986
8139917	48839503	8	~1986
8139959	16279919	8	~1985
8140133	195363193	9	~1988
8140211	16280423	8	~1985
8140211	65121689	8
8140439	16280879	8	~1985
8140571	16281143	8	~1985

Exp.	Prime Factor	Digits	Year
8140661	65125289	8	~1986
8141059	81410591	8	~1987
8141569	179114519	9	~1988
8141879	16283759	8	~1985
8141891	16283783	8	~1985
8141957	195406969	9	~1988
8142221	65137769	8	~1986
8142353	48854119	8	~1986
8142503	16285007	8	~1985
8142731	16285463	8	~1985
8142817	48856903	8	~1986
8143151	65145209	8	~1986
8143199	65145593	8	~1986
8143231	130291697	9	~1987
8143237	48859423	8	~1986
8143273	48859639	8	~1986
8143313	48859879	8	~1986
8143319	16286639	8	~1985
8143453	48860719	8	~1986
8143463	16286927	8	~1985
8143687	81436871	8	~1987
8143763	16287527	8	~1985
8143847	65150777	8	~1986
8143853	48863119	8	~1986
8143931	16287863	8	~1985

Exp.	Prime Factor	Digits	Year
8144039	16288079	8	~1985
8144237	48865423	8	~1986
8144291	16288583	8	~1985
8144393	48866359	8	~1986
8144399	16288799	8	~1985
8144579	16289159	8	~1985
8144861	48869167	8	~1986
8144951	65159609	8	~1986
8144999	65159993	8	~1986
8145209	65161673	8	~1986
8145419	16290839	8	~1985
8145443	16290887	8	~1985
8145479	16290959	8	~1985
8145541	48873247	8	~1986
8146511	16293023	8	~1985
8146571	16293143	8	~1985
8146637	48879823	8	~1986
8146751	16293503	8	~1985
8146867	472518287	9	~1989
8147047	81470471	8	~1987
8147101	48882607	8	~1986
8147123	16294247	8	~1985
8147291	65178329	8	~1986
8147351	65178809	8	~1986
8147417	195538009	9	~1988

Exp.	Prime Factor	Digits	Year
8147537	48885223	8	~1986
8147567	65180537	8	~1986
8147677	325907081	9	~1988
8147759	16295519	8	~1985
8147963	16295927	8	~1985
8148047	65184377	8	~1986
8148191	16296383	8	~1985
8148221	48889327	8	~1986
8148347	651867761	9	~1989
8148677	114081479	9	~1987
8148733	48892399	8	~1986
8148743	16297487	8	~1985
8149343	16298687	8	~1985
8149517	65196137	8	~1986
8149571	65196569	8	~1986
8149703	782371489	9	~1989
8149763	16299527	8	~1985
8149901	65199209	8	~1986
8149991	65199929	8	~1986
8150071	81500711	8	~1987
8150321	48901927	8	~1986
8150321	65202569	8
8150459	16300919	8	~1985
8150657	847668329	9	~1989
8150761	48904567	8	~1986

4.903.097 digits

25-07-08