Small Mersenne Prime Factors (page 949/5205)

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
8703257	69626057	8	~1987
8703551	417770449	9	~1989
8703613	52221679	8	~1986
8703659	17407319	8	~1985
8703743	17407487	8	~1985
8703911	17407823	8	~1985
8704183	1758244967	10	~1990
8704303	365580727	9	~1988
8704559	69636473	8	~1987
8704951	87049511	8	~1987
8705219	17410439	8	~1985
8705237	52231423	8	~1986
8705311	87053111	8	~1987
8705369	69642953	8	~1987
8705443	87054431	8	~1987
8705461	609382271	9	~1989
8705531	17411063	8	~1985
8705803	87058031	8	~1987
8705831	17411663	8	~1985
8706251	278600033	9	~1988
8706337	52238023	8	~1986
8706419	156715543	9	~1988
8706479	17412959	8	~1985
8706479	69651833	8
8706611	17413223	8	~1985

Exp.	Prime Factor	Digits	Year
8707241	52243447	8	~1986
8707607	208982569	9	~1988
8707631	17415263	8	~1985
8707763	17415527	8	~1985
8707793	52246759	8	~1986
8707877	52247263	8	~1986
8708069	278658209	9	~1988
8708081	52248487	8	~1986
8708527	139336433	9	~1987
8708537	69668297	8	~1987
8708663	17417327	8	~1985
8708831	17417663	8	~1985
8708969	69671753	8	~1987
8709383	17418767	8	~1985
8709443	17418887	8	~1985
8709553	261286591	9	~1988
8709713	52258279	8	~1986
8709971	17419943	8	~1985
8709973	52259839	8	~1986
8710061	69680489	8	~1987
8710193	52261159	8	~1986
8710277	52261663	8	~1986
8710333	52261999	8	~1986
8710343	17420687	8	~1985
8710567	209053609	9	~1988

Exp.	Prime Factor	Digits	Year
8710631	17421263	8	~1985
8710679	17421359	8	~1985
8710733	1045287961	10	~1990
8711051	17422103	8	~1985
8711083	87110831	8	~1987
8711347	348453881	9	~1988
8711401	52268407	8	~1986
8711561	52269367	8	~1986
8711741	69693929	8	~1987
8711777	52270663	8	~1986
8711987	156815767	9	~1988
8712181	52273087	8	~1986
8712259	87122591	8	~1987
8712337	52274023	8	~1986
8713007	69704057	8	~1987
8713583	17427167	8	~1985
8713643	17427287	8	~1985
8713811	17427623	8	~1985
8713931	17427863	8	~1985
8714003	17428007	8	~1985
8714021	69712169	8	~1987
8714491	348579641	9	~1988
8714903	17429807	8	~1985
8714963	17429927	8	~1985
8715023	17430047	8	~1985

Exp.	Prime Factor	Digits	Year
8715383	17430767	8	~1985
8715659	17431319	8	~1985
8715659	69725273	8
8716007	226616183	9	~1988
8716021	348640841	9	~1988
8716063	139457009	9	~1987
8716217	1255135249	10	~1990
8716271	17432543	8	~1985
8716439	17432879	8	~1985
8716531	139464497	9	~1987
8716627	87166271	8	~1987
8716703	17433407	8	~1985
8716997	52301983	8	~1986
8717117	52302703	8	~1986
8717123	17434247	8	~1985
8717557	1394809121	10	~1990
8717783	17435567	8	~1985
8717963	17435927	8	~1985
8717981	52307887	8	~1986
8718089	1952851937	10	~1990
8718191	17436383	8	~1985
8718401	52310407	8	~1986
8718427	209242249	9	~1988
8718431	17436863	8	~1985
8718491	17436983	8	~1985

4.903.097 digits

25-07-08