Small Mersenne Prime Factors (page 945/5025)

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
8850119	17700239	8	~1985
8850187	88501871	8	~1987
8850203	17700407	8	~1985
8850211	88502111	8	~1987
8850839	17701679	8	~1985
8850937	53105623	8	~1986
8851379	17702759	8	~1985
8851637	212439289	9	~1988
8851637	1557888113	10
8851723	212441353	9	~1988
8851727	159331087	9	~1988
8851763	17703527	8	~1985
8851813	53110879	8	~1986
8851949	1274680657	10	~1990
8852177	123930479	9	~1987
8852243	17704487	8	~1985
8852339	17704679	8	~1985
8852443	141639089	9	~1987
8852813	53116879	8	~1986
8852939	17705879	8	~1985
8853079	88530791	8	~1987
8853359	283307489	9	~1988
8853371	17706743	8	~1985
8853553	53121319	8	~1986
8853577	53121463	8	~1986

Exp.	Prime Factor	Digits	Year
8854453	53126719	8	~1986
8854691	17709383	8	~1985
8855009	70840073	8	~1987
8855123	17710247	8	~1985
8855137	53130823	8	~1986
8855771	17711543	8	~1985
8855921	53135527	8	~1986
8855941	425085169	9	~1989
8856131	17712263	8	~1985
8856361	53138167	8	~1986
8856557	53139343	8	~1986
8856713	53140279	8	~1986
8857091	17714183	8	~1985
8857159	88571591	8	~1987
8857259	17714519	8	~1985
8857817	53146903	8	~1986
8857873	53147239	8	~1986
8857883	17715767	8	~1985
8858257	53149543	8	~1986
8858483	17716967	8	~1985
8858711	159456799	9	~1988
8858957	53153743	8	~1986
8859127	88591271	8	~1987
8859197	53155183	8	~1986
8859299	17718599	8	~1985

Exp.	Prime Factor	Digits	Year
8859479	17718959	8	~1985
8859551	17719103	8	~1985
8859857	53159143	8	~1986
8859863	17719727	8	~1985
8860031	17720063	8	~1985
8860081	53160487	8	~1986
8860139	17720279	8	~1985
8860361	53162167	8	~1986
8860739	17721479	8	~1985
8860793	53164759	8	~1986
8860933	53165599	8	~1986
8861159	17722319	8	~1985
8861291	17722583	8	~1985
8861393	53168359	8	~1986
8861423	17722847	8	~1985
8861519	17723039	8	~1985
8861561	70892489	8	~1987
8861773	53170639	8	~1986
8861921	53171527	8	~1986
8862041	53172247	8	~1986
8862323	17724647	8	~1985
8862611	17725223	8	~1985
8862619	88626191	8	~1987
8863013	53178079	8	~1986
8863319	70906553	8	~1987

Exp.	Prime Factor	Digits	Year
8863333	53179999	8	~1986
8863499	17726999	8	~1985
8863619	17727239	8	~1985
8863691	17727383	8	~1985
8863703	17727407	8	~1985
8864291	17728583	8	~1985
8864351	17728703	8	~1985
8864417	53186503	8	~1986
8864461	53186767	8	~1986
8864903	17729807	8	~1985
8864969	336868823	9	~1988
8865011	17730023	8	~1985
8865203	17730407	8	~1985
8865443	17730887	8	~1985
8865583	212773993	9	~1988
8865763	141852209	9	~1987
8865803	17731607	8	~1985
8865991	88659911	8	~1987
8866079	17732159	8	~1985
8866079	70928633	8
8866147	88661471	8	~1987
8866391	17732783	8	~1985
8866463	17732927	8	~1985
8866603	88666031	8	~1987
8866667	70933337	8	~1987

4.724.182 digits

25-04-13