Small Mersenne Prime Factors (page 764/5025)

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
6111263	12222527	8	~1984
6111383	12222767	8	~1984
6111389	146673337	9	~1987
6111797	36670783	8	~1985
6112079	12224159	8	~1984
6112391	12224783	8	~1984
6112409	85573727	8	~1986
6112439	12224879	8	~1984
6112501	36675007	8	~1985
6112541	48900329	8	~1985
6112553	36675319	8	~1985
6112657	36675943	8	~1985
6112703	12225407	8	~1984
6112763	12225527	8	~1984
6112919	48903353	8	~1985
6112943	12225887	8	~1984
6113011	97808177	8	~1986
6113039	48904313	8	~1985
6113111	12226223	8	~1984
6113201	36679207	8	~1985
6113279	48906233	8	~1985
6113309	85586327	8	~1986
6113363	12226727	8	~1984
6114209	48913673	8	~1985
6114263	12228527	8	~1984

Exp.	Prime Factor	Digits	Year
6114539	12229079	8	~1984
6114593	36687559	8	~1985
6114623	12229247	8	~1984
6114767	48918137	8	~1985
6115001	48920009	8	~1985
6115337	36692023	8	~1985
6115513	36693079	8	~1985
6115547	48924377	8	~1985
6115877	330257359	9	~1987
6115909	183477271	9	~1987
6115979	48927833	8	~1985
6116161	36696967	8	~1985
6116647	61166471	8	~1986
6116699	12233399	8	~1984
6116717	48933737	8	~1985
6116833	36700999	8	~1985
6116953	36701719	8	~1985
6117341	36704047	8	~1985
6117389	636208457	9	~1988
6117491	12234983	8	~1984
6117599	12235199	8	~1984
6117641	48941129	8	~1985
6117851	12235703	8	~1984
6117901	183537031	9	~1987
6117919	61179191	8	~1986

Exp.	Prime Factor	Digits	Year
6117959	12235919	8	~1984
6117983	12235967	8	~1984
6118157	48945257	8	~1985
6118261	36709567	8	~1985
6118537	183556111	9	~1987
6118643	12237287	8	~1984
6118711	61187111	8	~1986
6118753	36712519	8	~1985
6118979	12237959	8	~1984
6119257	281485823	9	~1987
6119299	110147383	9	~1986
6119639	48957113	8	~1985
6119797	36718783	8	~1985
6119819	12239639	8	~1984
6119921	48959369	8	~1985
6120083	12240167	8	~1984
6120167	48961337	8	~1985
6120203	146884873	9	~1987
6120563	12241127	8	~1984
6120689	48965513	8	~1985
6120887	48967097	8	~1985
6121403	12242807	8	~1984
6121433	36728599	8	~1985
6121637	48973097	8	~1985
6121673	36730039	8	~1985

Exp.	Prime Factor	Digits	Year
6121877	36731263	8	~1985
6121877	85706279	8
6121919	12243839	8	~1984
6121919	110194543	9
6121931	1628433647	10	~1989
6122341	134691503	9	~1987
6122411	12244823	8	~1984
6122651	159188927	9	~1987
6122819	48982553	8	~1985
6122917	832716713	9	~1988
6122939	12245879	8	~1984
6122947	61229471	8	~1986
6122999	12245999	8	~1984
6122999	48983993	8
6123059	12246119	8	~1984
6123191	12246383	8	~1984
6123251	12246503	8	~1984
6123361	281674607	9	~1987
6123571	61235711	8	~1986
6123617	48988937	8	~1985
6123781	36742687	8	~1985
6124439	12248879	8	~1984
6124649	183739471	9	~1987
6124681	36748087	8	~1985
6124691	12249383	8	~1984

4.724.182 digits

25-04-13