Small Mersenne Prime Factors (page 938/5025)

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
8732351	69858809	8	~1987
8732489	69859913	8	~1987
8732653	52395919	8	~1986
8732819	17465639	8	~1985
8732879	17465759	8	~1985
8733083	17466167	8	~1985
8733251	17466503	8	~1985
8733259	349330361	9	~1988
8733541	52401247	8	~1986
8733547	768552137	9	~1989
8733551	17467103	8	~1985
8733743	17467487	8	~1985
8733839	17467679	8	~1985
8734223	17468447	8	~1985
8734841	52409047	8	~1986
8734919	17469839	8	~1985
8735341	262060231	9	~1988
8735429	69883433	8	~1987
8735621	52413727	8	~1986
8735711	17471423	8	~1985
8735849	69886793	8	~1987
8736179	17472359	8	~1985
8736263	17472527	8	~1985
8736659	17473319	8	~1985
8736719	17473439	8	~1985

Exp.	Prime Factor	Digits	Year
8737139	17474279	8	~1985
8737271	17474543	8	~1985
8737357	52424143	8	~1986
8737483	87374831	8	~1987
8737763	17475527	8	~1985
8737829	69902633	8	~1987
8737979	17475959	8	~1985
8738033	279617057	9	~1988
8738231	17476463	8	~1985
8738351	17476703	8	~1985
8738363	17476727	8	~1985
8738377	52430263	8	~1986
8738591	17477183	8	~1985
8738711	17477423	8	~1985
8738759	17477519	8	~1985
8738783	17477567	8	~1985
8738843	367031407	9	~1988
8738957	52433743	8	~1986
8738963	17477927	8	~1985
8739001	52434007	8	~1986
8739023	17478047	8	~1985
8739119	17478239	8	~1985
8739299	17478599	8	~1985
8739431	17478863	8	~1985
8739803	17479607	8	~1985

Exp.	Prime Factor	Digits	Year
8739877	139838033	9	~1987
8739953	52439719	8	~1986
8740037	69920297	8	~1987
8740163	17480327	8	~1985
8740541	52443247	8	~1986
8740681	52444087	8	~1986
8740727	1258664689	10	~1990
8740859	17481719	8	~1985
8740871	17481743	8	~1985
8740993	52445959	8	~1986
8741303	17482607	8	~1985
8741699	17483399	8	~1985
8741801	52450807	8	~1986
8741861	52451167	8	~1986
8742551	17485103	8	~1985
8742577	52455463	8	~1986
8742787	87427871	8	~1987
8743019	17486039	8	~1985
8743037	52458223	8	~1986
8743037	69944297	8
8743043	17486087	8	~1985
8743213	52459279	8	~1986
8743547	157383847	9	~1988
8743583	17487167	8	~1985
8743589	69948713	8	~1987

Exp.	Prime Factor	Digits	Year
8743633	472156183	9	~1989
8743681	52462087	8	~1986
8743817	69950537	8	~1987
8743991	17487983	8	~1985
8744033	52464199	8	~1986
8744447	69955577	8	~1987
8744513	1049341561	10	~1990
8744707	87447071	8	~1987
8744831	17489663	8	~1985
8744903	17489807	8	~1985
8745557	69964457	8	~1987
8745827	157424887	9	~1988
8745929	69967433	8	~1987
8746037	52476223	8	~1986
8746093	52476559	8	~1986
8746301	52477807	8	~1986
8746399	87463991	8	~1987
8746399	157435183	9
8746733	52480399	8	~1986
8746757	52480543	8	~1986
8746799	17493599	8	~1985
8747159	17494319	8	~1985
8747243	17494487	8	~1985
8747423	17494847	8	~1985
8748011	17496023	8	~1985

4.724.182 digits

25-04-13