Small Mersenne Prime Factors (page 992/5670)

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
8921249	71369993	8	~1987
8921441	53528647	8	~1986
8921663	17843327	8	~1985
8921761	53530567	8	~1986
8921771	17843543	8	~1985
8922041	71376329	8	~1987
8922107	71376857	8	~1987
8922233	53533399	8	~1986
8922257	71378057	8	~1987
8922313	142757009	9	~1987
8922359	71378873	8	~1987
8922377	71379017	8	~1987
8922443	17844887	8	~1985
8922449	124914287	9	~1987
8922577	142761233	9	~1987
8922601	53535607	8	~1986
8922659	17845319	8	~1985
8922869	124920167	9	~1987
8923049	71384393	8	~1987
8923073	53538439	8	~1986
8923267	160618807	9	~1988
8923357	53540143	8	~1986
8923639	89236391	8	~1987
8923807	214171369	9	~1988
8923961	1624160903	10	~1990

Exp.	Prime Factor	Digits	Year
8923991	17847983	8	~1985
8924011	89240111	8	~1987
8924089	6407495903	10	~1992
8924309	285577889	9	~1988
8924387	71395097	8	~1987
8924411	17848823	8	~1985
8924579	17849159	8	~1985
8924701	53548207	8	~1986
8925047	71400377	8	~1987
8925131	17850263	8	~1985
8925181	53551087	8	~1986
8925419	17850839	8	~1985
8925557	214213369	9	~1988
8925599	17851199	8	~1985
8925797	53554783	8	~1986
8925803	17851607	8	~1985
8925809	428438833	9	~1989
8925887	71407097	8	~1987
8925977	53555863	8	~1986
8926061	71408489	8	~1987
8926331	17852663	8	~1985
8926517	71412137	8	~1987
8927341	53564047	8	~1986
8927357	71418857	8	~1987
8927441	53564647	8	~1986

Exp.	Prime Factor	Digits	Year
8927489	267824671	9	~1988
8927813	53566879	8	~1986
8927833	53566999	8	~1986
8928131	17856263	8	~1985
8928173	53569039	8	~1986
8928191	17856383	8	~1985
8928371	17856743	8	~1985
8928749	71429993	8	~1987
8928851	17857703	8	~1985
8928863	17857727	8	~1985
8929139	71433113	8	~1987
8929331	17858663	8	~1985
8930021	53580127	8	~1986
8930179	89301791	8	~1987
8930351	71442809	8	~1987
8930591	17861183	8	~1985
8930849	214340377	9	~1988
8930951	17861903	8	~1985
8931037	53586223	8	~1986
8931119	17862239	8	~1985
8931119	214346857	9
8931421	53588527	8	~1986
8931431	17862863	8	~1985
8931523	1875619831	10	~1990
8931683	17863367	8	~1985

Exp.	Prime Factor	Digits	Year
8931731	17863463	8	~1985
8931757	53590543	8	~1986
8932117	53592703	8	~1986
8932139	17864279	8	~1985
8932271	17864543	8	~1985
8932457	53594743	8	~1986
8932481	53594887	8	~1986
8932733	53596399	8	~1986
8932883	17865767	8	~1985
8933231	17866463	8	~1985
8933297	267998911	9	~1988
8933339	17866679	8	~1985
8933437	53600623	8	~1986
8933569	268007071	9	~1988
8933623	89336231	8	~1987
8934071	17868143	8	~1985
8934083	17868167	8	~1985
8934173	53605039	8	~1986
8934287	71474297	8	~1987
8934521	71476169	8	~1987
8934631	89346311	8	~1987
8934743	17869487	8	~1985
8935021	196570463	9	~1988
8935231	160834159	9	~1988
8935313	53611879	8	~1986

5.366.787 digits

26-02-08