Small Mersenne Prime Factors (page 515/5190)

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
3137573	43926023	8	~1984
3137663	6275327	7	~1982
3137669	25101353	8	~1983
3137747	25101977	8	~1983
3137749	75305977	8	~1984
3137837	18827023	8	~1983
3137941	18827647	8	~1983
3137999	6275999	7	~1982
3138041	25104329	8	~1983
3138071	6276143	7	~1982
3138361	18830167	8	~1983
3138449	43938287	8	~1984
3138521	25108169	8	~1983
3138593	18831559	8	~1983
3138671	56496079	8	~1984
3138799	31387991	8	~1983
3138851	6277703	7	~1982
3138911	6277823	7	~1982
3139111	56503999	8	~1984
3139403	6278807	7	~1982
3139471	31394711	8	~1983
3139597	18837583	8	~1983
3139621	18837727	8	~1983
3139621	94188631	8
3139919	6279839	7	~1982

Exp.	Prime Factor	Digits	Year
3139991	6279983	7	~1982
3140041	18840247	8	~1983
3140099	6280199	7	~1982
3140183	6280367	7	~1982
3140243	6280487	7	~1982
3140317	50245073	8	~1984
3140653	18843919	8	~1983
3140701	94221031	8	~1985
3140717	43970039	8	~1984
3140783	6281567	7	~1982
3140807	25126457	8	~1983
3140911	376909321	9	~1986
3140933	18845599	8	~1983
3140933	75382393	8
3141283	31412831	8	~1983
3141319	31413191	8	~1983
3141371	6282743	7	~1982
3141473	18848839	8	~1983
3141557	43981799	8	~1984
3141647	25133177	8	~1983
3141877	18851263	8	~1983
3141883	31418831	8	~1983
3141899	6283799	7	~1982
3141959	6283919	7	~1982
3142259	6284519	7	~1982

Exp.	Prime Factor	Digits	Year
3142259	25138073	8
3142333	18853999	8	~1983
3142393	18854359	8	~1983
3142393	69132647	8
3142453	50279249	8	~1984
3142709	25141673	8	~1983
3142963	50287409	8	~1984
3143141	25145129	8	~1983
3143243	6286487	7	~1982
3143299	31432991	8	~1983
3143299	1037288671	10
3143549	150890353	9	~1985
3143771	6287543	7	~1982
3144059	6288119	7	~1982
3144059	56593063	8
3144067	861474359	9	~1987
3144083	6288167	7	~1982
3144143	6288287	7	~1982
3144157	50306513	8	~1984
3144217	18865303	8	~1983
3144259	13482582593	11	~1990
3144539	6289079	7	~1982
3144761	245291359	9	~1986
3144907	31449071	8	~1983
3145091	81772367	8	~1984

Exp.	Prime Factor	Digits	Year
3145097	18870583	8	~1983
3145283	6290567	7	~1982
3145283	75486793	8
3145553	44037743	8	~1984
3145559	6291119	7	~1982
3145559	25164473	8
3145873	18875239	8	~1983
3145903	31459031	8	~1983
3146021	18876127	8	~1983
3146041	245391199	9	~1986
3146183	6292367	7	~1982
3146237	25169897	8	~1983
3146243	157312151	9	~1985
3146303	6292607	7	~1982
3146399	25171193	8	~1983
3146459	6292919	7	~1982
3146483	157324151	9	~1985
3146501	25172009	8	~1983
3146771	176219177	9	~1985
3146867	25174937	8	~1983
3146953	18881719	8	~1983
3146987	56645767	8	~1984
3147121	18882727	8	~1983
3147169	94415071	8	~1985
3147197	44060759	8	~1984

4.888.230 digits

25-06-29