Small Mersenne Prime Factors (page 507/5070)

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
3097739	6195479	7	~1982
3097781	2032144337	10	~1988
3098153	18588919	8	~1983
3098299	74359177	8	~1984
3098423	6196847	7	~1982
3098597	18591583	8	~1983
3098687	24789497	8	~1983
3098723	6197447	7	~1982
3098747	24789977	8	~1983
3098789	24790313	8	~1983
3098999	6197999	7	~1982
3099029	24792233	8	~1983
3099059	6198119	7	~1982
3099179	6198359	7	~1982
3099193	49587089	8	~1984
3099293	74383033	8	~1984
3099359	6198719	7	~1982
3099617	18597703	8	~1983
3099911	24799289	8	~1983
3100127	24801017	8	~1983
3100151	6200303	7	~1982
3100199	6200399	7	~1982
3100289	43404047	8	~1984
3100367	24802937	8	~1983
3100661	117825119	9	~1985

Exp.	Prime Factor	Digits	Year
3100739	6201479	7	~1982
3100843	31008431	8	~1983
3100913	93027391	8	~1985
3100939	55816903	8	~1984
3100991	6201983	7	~1982
3100991	155049551	9
3101051	6202103	7	~1982
3101183	6202367	7	~1982
3101207	24809657	8	~1983
3101291	6202583	7	~1982
3101311	124052441	9	~1985
3101479	552063263	9	~1986
3101591	24812729	8	~1983
3101653	49626449	8	~1984
3101653	124066121	9
3101743	49627889	8	~1984
3101771	6203543	7	~1982
3101827	74443849	8	~1984
3101831	6203663	7	~1982
3101897	24815177	8	~1983
3101951	6203903	7	~1982
3101957	74446969	8	~1984
3102017	18612103	8	~1983
3102059	6204119	7	~1982
3102181	18613087	8	~1983

Exp.	Prime Factor	Digits	Year
3102269	24818153	8	~1983
3102353	18614119	8	~1983
3102431	24819449	8	~1983
3102481	18614887	8	~1983
3102503	6205007	7	~1982
3102877	49646033	8	~1984
3102929	43441007	8	~1984
3103021	49648337	8	~1984
3103033	18618199	8	~1983
3103211	6206423	7	~1982
3103241	24825929	8	~1983
3103381	49654097	8	~1984
3103553	18621319	8	~1983
3103579	31035791	8	~1983
3103579	55864423	8
3103589	322773257	9	~1986
3103679	24829433	8	~1983
3103687	701433263	9	~1987
3103757	18622543	8	~1983
3103799	6207599	7	~1982
3103801	49660817	8	~1984
3103817	24830537	8	~1983
3103829	24830633	8	~1983
3103861	18623167	8	~1983
3104063	6208127	7	~1982

Exp.	Prime Factor	Digits	Year
3104099	6208199	7	~1982
3104533	18627199	8	~1983
3104767	31047671	8	~1983
3104833	68306327	8	~1984
3104903	6209807	7	~1982
3105041	18630247	8	~1983
3105107	24840857	8	~1983
3105269	74526457	8	~1984
3105419	6210839	7	~1982
3105433	49686929	8	~1984
3105491	6210983	7	~1982
3105527	24844217	8	~1983
3105703	31057031	8	~1983
3105841	18635047	8	~1983
3105979	180146783	9	~1985
3106003	31060031	8	~1983
3106003	124240121	9
3106073	74545753	8	~1984
3106079	6212159	7	~1982
3106199	24849593	8	~1983
3106273	18637639	8	~1983
3106307	24850457	8	~1983
3106319	74551657	8	~1984
3106381	49702097	8	~1984
3106381	93191431	8

4.768.925 digits

25-05-04