Small Mersenne Prime Factors (page 909/5025)

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
8250257	115503599	9	~1987
8250323	16500647	8	~1985
8250329	66002633	8	~1986
8250397	198009529	9	~1988
8250497	49502983	8	~1986
8251121	49506727	8	~1986
8251151	16502303	8	~1985
8251351	82513511	8	~1987
8251601	66012809	8	~1986
8251717	49510303	8	~1986
8251751	16503503	8	~1985
8251949	115527287	9	~1987
8252351	16504703	8	~1985
8252359	148542463	9	~1987
8252533	49515199	8	~1986
8252551	82525511	8	~1987
8252681	313601879	9	~1988
8252807	148550527	9	~1987
8252941	49517647	8	~1986
8253031	82530311	8	~1987
8253053	49518319	8	~1986
8253101	49518607	8	~1986
8253373	49520239	8	~1986
8253863	16507727	8	~1985
8253911	16507823	8	~1985

Exp.	Prime Factor	Digits	Year
8253977	49523863	8	~1986
8254019	16508039	8	~1985
8254297	49525783	8	~1986
8254439	16508879	8	~1985
8254577	49527463	8	~1986
8254693	49528159	8	~1986
8254859	16509719	8	~1985
8254871	16509743	8	~1985
8255029	330201161	9	~1988
8255171	66041369	8	~1986
8255363	16510727	8	~1985
8255399	16510799	8	~1985
8255453	49532719	8	~1986
8255561	2575735033	10	~1990
8255657	66045257	8	~1986
8255711	16511423	8	~1985
8255771	148603879	9	~1987
8255939	198142537	9	~1988
8256233	49537399	8	~1986
8256779	16513559	8	~1985
8256863	16513727	8	~1985
8257237	247717111	9	~1988
8257643	16515287	8	~1985
8257757	49546543	8	~1986
8258099	66064793	8	~1986

Exp.	Prime Factor	Digits	Year
8258303	16516607	8	~1985
8258333	49549999	8	~1986
8258543	16517087	8	~1985
8258717	49552303	8	~1986
8258737	49552423	8	~1986
8258819	16517639	8	~1985
8258903	16517807	8	~1985
8258951	16517903	8	~1985
8259067	82590671	8	~1987
8259143	16518287	8	~1985
8259479	16518959	8	~1985
8259551	16519103	8	~1985
8259683	16519367	8	~1985
8259743	16519487	8	~1985
8260073	49560439	8	~1986
8260457	49562743	8	~1986
8260807	132172913	9	~1987
8260883	16521767	8	~1985
8260919	16521839	8	~1985
8260919	66087353	8
8261243	413062151	9	~1988
8261339	16522679	8	~1985
8261359	148704463	9	~1987
8261501	66092009	8	~1986
8261843	16523687	8	~1985

Exp.	Prime Factor	Digits	Year
8261857	49571143	8	~1986
8261999	16523999	8	~1985
8262179	16524359	8	~1985
8262179	66097433	8
8262193	49573159	8	~1986
8262227	66097817	8	~1986
8262343	1784666089	10	~1990
8262431	16524863	8	~1985
8262481	49574887	8	~1986
8262757	49576543	8	~1986
8262811	148730599	9	~1987
8262841	132205457	9	~1987
8262937	49577623	8	~1986
8263183	82631831	8	~1987
8263379	16526759	8	~1985
8263441	49580647	8	~1986
8263511	16527023	8	~1985
8263523	16527047	8	~1985
8263571	16527143	8	~1985
8263823	16527647	8	~1985
8264387	396690577	9	~1988
8264783	16529567	8	~1985
8265121	49590727	8	~1986
8265311	16530623	8	~1985
8265407	66123257	8	~1986

4.724.182 digits

25-04-13