Small Mersenne Prime Factors (page 884/4665)

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
8261843	16523687	8	~1985
8261857	49571143	8	~1986
8261999	16523999	8	~1985
8262179	16524359	8	~1985
8262179	66097433	8
8262193	49573159	8	~1986
8262227	66097817	8	~1986
8262343	1784666089	10	~1990
8262431	16524863	8	~1985
8262481	49574887	8	~1986
8262757	49576543	8	~1986
8262841	132205457	9	~1987
8262937	49577623	8	~1986
8263183	82631831	8	~1987
8263379	16526759	8	~1985
8263441	49580647	8	~1986
8263511	16527023	8	~1985
8263523	16527047	8	~1985
8263571	16527143	8	~1985
8263823	16527647	8	~1985
8264387	396690577	9	~1988
8264783	16529567	8	~1985
8265121	49590727	8	~1986
8265311	16530623	8	~1985
8265407	66123257	8	~1986

Exp.	Prime Factor	Digits	Year
8265431	16530863	8	~1985
8265539	16531079	8	~1985
8265833	49594999	8	~1986
8265919	82659191	8	~1987
8265973	132255569	9	~1987
8265979	82659791	8	~1987
8266129	181854839	9	~1988
8266373	115729223	9	~1987
8266513	49599079	8	~1986
8266931	16533863	8	~1985
8267339	66138713	8	~1986
8267351	16534703	8	~1985
8267951	16535903	8	~1985
8268241	49609447	8	~1986
8268497	49610983	8	~1986
8268803	16537607	8	~1985
8268893	115764503	9	~1987
8268899	66151193	8	~1986
8268913	49613479	8	~1986
8269013	49614079	8	~1986
8269043	16538087	8	~1985
8269439	66155513	8	~1986
8269559	16539119	8	~1985
8269619	16539239	8	~1985
8269711	132315377	9	~1987

Exp.	Prime Factor	Digits	Year
8269763	16539527	8	~1985
8270033	49620199	8	~1986
8270039	198480937	9	~1988
8270201	49621207	8	~1986
8270671	148872079	9	~1987
8270711	16541423	8	~1985
8270881	49625287	8	~1986
8271049	181963079	9	~1988
8271521	49629127	8	~1986
8271839	16543679	8	~1985
8271841	49631047	8	~1986
8272097	115809359	9	~1987
8272177	49633063	8	~1986
8272403	16544807	8	~1985
8272483	132359729	9	~1987
8272681	49636087	8	~1986
8272763	16545527	8	~1985
8272787	215092463	9	~1988
8272861	248185831	9	~1988
8273453	49640719	8	~1986
8273579	16547159	8	~1985
8273773	49642639	8	~1986
8273879	16547759	8	~1985
8274023	16548047	8	~1985
8274137	66193097	8	~1986

Exp.	Prime Factor	Digits	Year
8274239	16548479	8	~1985
8274547	1125338393	10	~1989
8274559	82745591	8	~1987
8274677	49648063	8	~1986
8274901	49649407	8	~1986
8275133	198603193	9	~1988
8275213	331008521	9	~1988
8275343	16550687	8	~1985
8275381	49652287	8	~1986
8275439	16550879	8	~1985
8275439	198610537	9
8275451	16550903	8	~1985
8275601	49653607	8	~1986
8276351	16552703	8	~1985
8276591	16553183	8	~1985
8276693	49660159	8	~1986
8276693	1853979233	10
8276713	49660279	8	~1986
8276797	49660783	8	~1986
8277323	16554647	8	~1985
8277617	49665703	8	~1986
8277653	49665919	8	~1986
8277697	132443153	9	~1987
8277707	463551593	9	~1989
8277719	16555439	8	~1985

4.368.158 digits

24-10-27