Small Mersenne Prime Factors (page 528/5850)

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
3101957	74446969	8	~1984
3102017	18612103	8	~1983
3102059	6204119	7	~1982
3102181	18613087	8	~1983
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

Exp.	Prime Factor	Digits	Year
3103817	24830537	8	~1983
3103829	24830633	8	~1983
3103861	18623167	8	~1983
3104063	6208127	7	~1982
3104099	6208199	7	~1982
3104267	173838953	9	~1985
3104533	18627199	8	~1983
3104767	31047671	8	~1983
3104833	68306327	8	~1984
3104903	6209807	7	~1982
3105041	18630247	8	~1983
3105107	24840857	8	~1983
3105119	74522857	8	~1984
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

Exp.	Prime Factor	Digits	Year
3106199	24849593	8	~1983
3106273	18637639	8	~1983
3106307	24850457	8	~1983
3106319	74551657	8	~1984
3106381	49702097	8	~1984
3106381	93191431	8
3106429	68341439	8	~1984
3106643	6213287	7	~1982
3106703	6213407	7	~1982
3106751	6213503	7	~1982
3106777	49708433	8	~1984
3106849	571660217	9	~1987
3106919	6213839	7	~1982
3107033	18642199	8	~1983
3107081	24856649	8	~1983
3107171	24857369	8	~1983
3107249	24857993	8	~1983
3107483	372897961	9	~1986
3107633	18645799	8	~1983
3107711	6215423	7	~1982
3107827	49725233	8	~1984
3107893	18647359	8	~1983
3107927	74590249	8	~1984
3108019	74592457	8	~1984
3108023	6216047	7	~1982

Exp.	Prime Factor	Digits	Year
3108067	55945207	8	~1984
3108239	6216479	7	~1982
3108239	55948303	8
3108359	6216719	7	~1982
3108359	24866873	8
3108373	18650239	8	~1983
3108461	18650767	8	~1983
3108551	6217103	7	~1982
3108737	93262111	8	~1985
3108779	24870233	8	~1983
3108893	18653359	8	~1983
3109031	24872249	8	~1983
3109069	93272071	8	~1985
3109091	80836367	8	~1984
3109159	31091591	8	~1983
3109193	18655159	8	~1983
3109307	149246737	9	~1985
3109333	18655999	8	~1983
3109333	68405327	8
3109343	6218687	7	~1982
3109349	43530887	8	~1984
3109397	18656383	8	~1983
3109411	31094111	8	~1983
3109441	18656647	8	~1983
3109619	24876953	8	~1983

5.546.121 digits

26-05-03