Small Mersenne Prime Factors (page 539/5445)

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
3304751	6609503	7	~1982
3304913	19829479	8	~1983
3305017	19830103	8	~1983
3305171	6610343	7	~1982
3305257	152041823	9	~1985
3305279	6610559	7	~1982
3305303	6610607	7	~1982
3305581	19833487	8	~1983
3305699	6611399	7	~1982
3305759	6611519	7	~1982
3305851	59505319	8	~1984
3306059	6612119	7	~1982
3306137	19836823	8	~1983
3306239	6612479	7	~1982
3306467	59516407	8	~1984
3306659	6613319	7	~1982
3306679	33066791	8	~1984
3306847	33068471	8	~1984
3306911	6613823	7	~1982
3306913	231483911	9	~1986
3306977	19841863	8	~1983
3307141	72757103	8	~1984
3307201	99216031	8	~1985
3307211	6614423	7	~1982
3307327	59531887	8	~1984

Exp.	Prime Factor	Digits	Year
3307327	793758481	9
3307379	6614759	7	~1982
3307439	6614879	7	~1982
3307523	6615047	7	~1982
3307567	33075671	8	~1984
3307631	6615263	7	~1982
3307663	317535649	9	~1986
3307831	52925297	8	~1984
3307939	33079391	8	~1984
3308027	59544487	8	~1984
3308161	19848967	8	~1983
3308273	19849639	8	~1983
3308303	6616607	7	~1982
3308381	19850287	8	~1983
3308509	99255271	8	~1985
3308653	19851919	8	~1983
3308663	6617327	7	~1982
3308867	26470937	8	~1983
3308917	19853503	8	~1983
3308939	26471513	8	~1983
3308957	26471657	8	~1983
3308989	231629231	9	~1986
3309037	79416889	8	~1985
3309413	19856479	8	~1983
3309541	19857247	8	~1983

Exp.	Prime Factor	Digits	Year
3309703	52955249	8	~1984
3309991	52959857	8	~1984
3310201	19861207	8	~1983
3310663	33106631	8	~1984
3310799	26486393	8	~1983
3310861	52973777	8	~1984
3311051	26488409	8	~1983
3311219	26489753	8	~1983
3311411	6622823	7	~1982
3311579	6623159	7	~1982
3311983	112607423	9	~1985
3312097	19872583	8	~1983
3312217	19873303	8	~1983
3312503	6625007	7	~1982
3312601	19875607	8	~1983
3312623	6625247	7	~1982
3312697	19876183	8	~1983
3312733	19876399	8	~1983
3312733	53003729	8
3312737	26501897	8	~1983
3312941	19877647	8	~1983
3313067	26504537	8	~1983
3313067	59635207	8
3313183	33131831	8	~1984
3313319	6626639	7	~1982

Exp.	Prime Factor	Digits	Year
3313573	19881439	8	~1983
3313697	26509577	8	~1983
3313823	106042337	9	~1985
3313837	53021393	8	~1984
3313879	59649823	8	~1984
3313883	6627767	7	~1982
3313957	152442023	9	~1985
3314147	26513177	8	~1983
3314257	19885543	8	~1983
3314383	53030129	8	~1984
3314429	46402007	8	~1984
3314459	26515673	8	~1983
3314471	6628943	7	~1982
3314639	6629279	7	~1982
3314687	79552489	8	~1985
3314713	19888279	8	~1983
3314917	53038673	8	~1984
3314963	6629927	7	~1982
3315007	33150071	8	~1984
3315031	33150311	8	~1984
3315031	53040497	8
3315073	19890439	8	~1983
3315079	33150791	8	~1984
3315131	26521049	8	~1983
3315131	59672359	8

5.142.307 digits

25-10-26