Small Mersenne Prime Factors (page 519/5340)

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
3133019	75192457	8	~1984
3133057	18798343	8	~1983
3133177	18799063	8	~1983
3133211	6266423	7	~1982
3133279	56399023	8	~1984
3133337	25066697	8	~1983
3133397	25067177	8	~1983
3133441	68935703	8	~1984
3133463	6266927	7	~1982
3133721	194290703	9	~1985
3133751	25070009	8	~1983
3133891	31338911	8	~1983
3134023	75216553	8	~1984
3134063	6268127	7	~1982
3134123	6268247	7	~1982
3134213	18805279	8	~1983
3134213	43878983	8
3134347	50149553	8	~1984
3134447	56420047	8	~1984
3134519	25076153	8	~1983
3134557	18807343	8	~1983
3134633	2808631169	10	~1988
3134797	50156753	8	~1984
3134801	2884016921	10	~1988
3134903	6269807	7	~1982

Exp.	Prime Factor	Digits	Year
3135071	25080569	8	~1983
3135403	50166449	8	~1984
3135469	376256281	9	~1986
3135571	31355711	8	~1983
3135623	6271247	7	~1982
3136319	6272639	7	~1982
3136457	25091657	8	~1983
3136531	56457559	8	~1984
3136571	56458279	8	~1984
3136631	6273263	7	~1982
3136649	25093193	8	~1983
3136667	25093337	8	~1983
3136877	25095017	8	~1983
3136933	18821599	8	~1983
3137117	94113511	8	~1985
3137257	18823543	8	~1983
3137371	31373711	8	~1983
3137389	69022559	8	~1984
3137399	6274799	7	~1982
3137521	18825127	8	~1983
3137573	43926023	8	~1984
3137663	6275327	7	~1982
3137669	25101353	8	~1983
3137747	25101977	8	~1983
3137749	75305977	8	~1984

Exp.	Prime Factor	Digits	Year
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
3139991	6279983	7	~1982
3140041	18840247	8	~1983
3140099	6280199	7	~1982
3140183	6280367	7	~1982
3140243	6280487	7	~1982

Exp.	Prime Factor	Digits	Year
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
3142259	25138073	8
3142333	18853999	8	~1983
3142393	18854359	8	~1983
3142393	69132647	8
3142453	50279249	8	~1984

5.037.460 digits

25-09-07