Small Mersenne Prime Factors (page 918/4665)

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
8843903	17687807	8	~1985
8844127	141506033	9	~1987
8844239	70753913	8	~1987
8844263	17688527	8	~1985
8844377	123821279	9	~1987
8844659	17689319	8	~1985
8844779	17689559	8	~1985
8844911	17689823	8	~1985
8845451	17690903	8	~1985
8845861	53075167	8	~1986
8845937	53075623	8	~1986
8846063	17692127	8	~1985
8846231	17692463	8	~1985
8846291	17692583	8	~1985
8846317	141541073	9	~1987
8846353	53078119	8	~1986
8846483	17692967	8	~1985
8846641	53079847	8	~1986
8846963	17693927	8	~1985
8847557	477768079	9	~1989
8847593	53085559	8	~1986
8847691	88476911	8	~1987
8847719	17695439	8	~1985
8847731	17695463	8	~1985
8848027	212352649	9	~1988

Exp.	Prime Factor	Digits	Year
8848139	17696279	8	~1985
8848379	17696759	8	~1985
8848453	141575249	9	~1987
8848589	70788713	8	~1987
8849063	17698127	8	~1985
8849257	53095543	8	~1986
8849371	141589937	9	~1987
8849531	17699063	8	~1985
8849591	17699183	8	~1985
8849903	17699807	8	~1985
8850011	70800089	8	~1987
8850113	53100679	8	~1986
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

Exp.	Prime Factor	Digits	Year
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
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
8856131	17712263	8	~1985
8856361	53138167	8	~1986
8856557	53139343	8	~1986
8856713	53140279	8	~1986
8857091	17714183	8	~1985
8857159	88571591	8	~1987

Exp.	Prime Factor	Digits	Year
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
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

4.368.158 digits

24-10-27