Small Mersenne Prime Factors (page 959/5340)

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
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
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

Exp.	Prime Factor	Digits	Year
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
8714231	69713849	8	~1987
8714491	348579641	9	~1988
8714903	17429807	8	~1985
8714963	17429927	8	~1985
8715023	17430047	8	~1985
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

Exp.	Prime Factor	Digits	Year
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
8718539	69748313	8	~1987
8718733	52312399	8	~1986
8718737	52312423	8	~1986
8718811	87188111	8	~1987
8719127	69753017	8	~1987
8719133	52314799	8	~1986
8719211	17438423	8	~1985
8719253	52315519	8	~1986
8719303	209263273	9	~1988

Exp.	Prime Factor	Digits	Year
8719391	17438783	8	~1985
8719831	156956959	9	~1988
8719873	558071873	9	~1989
8720171	17440343	8	~1985
8720311	87203111	8	~1987
8720483	17440967	8	~1985
8720533	52323199	8	~1986
8721029	69768233	8	~1987
8721101	331401839	9	~1988
8721239	17442479	8	~1985
8721239	69769913	8
8721607	348864281	9	~1988
8721749	1378036343	10	~1990
8721763	139548209	9	~1987
8721913	52331479	8	~1986
8722097	52332583	8	~1986
8722409	69779273	8	~1987
8722607	69780857	8	~1987
8722799	17445599	8	~1985
8723063	17446127	8	~1985
8723213	52339279	8	~1986
8723321	69786569	8	~1987
8723441	52340647	8	~1986
8723459	69787673	8	~1987
8723531	17447063	8	~1985

5.037.460 digits

25-09-07