Small Mersenne Prime Factors (page 841/5025)

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
7199411	14398823	8	~1985
7199519	14399039	8	~1985
7200101	43200607	8	~1986
7200121	43200727	8	~1986
7200131	14400263	8	~1985
7200191	14400383	8	~1985
7200923	14401847	8	~1985
7201157	57609257	8	~1986
7201427	57611417	8	~1986
7201583	14403167	8	~1985
7201823	14403647	8	~1985
7201981	43211887	8	~1986
7202099	14404199	8	~1985
7202579	14405159	8	~1985
7202597	57620777	8	~1986
7202641	43215847	8	~1986
7202711	14405423	8	~1985
7202963	14405927	8	~1985
7202999	14405999	8	~1985
7203193	43219159	8	~1986
7203227	57625817	8	~1986
7203263	14406527	8	~1985
7203289	734735479	9	~1989
7203491	14406983	8	~1985
7203491	57627929	8

Exp.	Prime Factor	Digits	Year
7203697	43222183	8	~1986
7203743	14407487	8	~1985
7203881	43223287	8	~1986
7203979	244935287	9	~1988
7204061	57632489	8	~1986
7204133	43224799	8	~1986
7204201	43225207	8	~1986
7204271	14408543	8	~1985
7204273	43225639	8	~1986
7204391	57635129	8	~1986
7204777	115276433	9	~1987
7205171	14410343	8	~1985
7205183	14410367	8	~1985
7205347	115285553	9	~1987
7205461	43232767	8	~1986
7205533	115288529	9	~1987
7205641	158524103	9	~1987
7205753	100880543	9	~1987
7205771	14411543	8	~1985
7205843	14411687	8	~1985
7206191	14412383	8	~1985
7206197	57649577	8	~1986
7206203	14412407	8	~1985
7206977	216209311	9	~1987
7207037	57656297	8	~1986

Exp.	Prime Factor	Digits	Year
7207181	57657449	8	~1986
7207331	57658649	8	~1986
7207619	14415239	8	~1985
7207661	43245967	8	~1986
7207757	43246543	8	~1986
7207883	14415767	8	~1985
7207919	14415839	8	~1985
7208317	43249903	8	~1986
7208711	14417423	8	~1985
7208717	100922039	9	~1987
7208759	14417519	8	~1985
7209259	72092591	8	~1986
7209533	100933463	9	~1987
7209539	14419079	8	~1985
7209551	14419103	8	~1985
7209757	43258543	8	~1986
7209877	43259263	8	~1986
7210061	57680489	8	~1986
7210433	43262599	8	~1986
7210453	43262719	8	~1986
7210663	72106631	8	~1986
7210751	14421503	8	~1985
7210811	14421623	8	~1985
7210943	14421887	8	~1985
7210991	14421983	8	~1985

Exp.	Prime Factor	Digits	Year
7211011	288440441	9	~1988
7211201	43267207	8	~1986
7211201	57689609	8
7211273	43267639	8	~1986
7211291	57690329	8	~1986
7211333	43267999	8	~1986
7211381	43268287	8	~1986
7211639	57693113	8	~1986
7211843	14423687	8	~1985
7211977	43271863	8	~1986
7212169	173092057	9	~1987
7212173	43273039	8	~1986
7212253	43273519	8	~1986
7212323	14424647	8	~1985
7212719	57701753	8	~1986
7212791	14425583	8	~1985
7212791	57702329	8
7212839	14425679	8	~1985
7212899	14425799	8	~1985
7213441	43280647	8	~1986
7213567	115417073	9	~1987
7213571	57708569	8	~1986
7213751	14427503	8	~1985
7213847	57710777	8	~1986
7214063	187565639	9	~1987

4.724.182 digits

25-04-13