Small Mersenne Prime Factors (page 699/5025)

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
5270773	31624639	8	~1985
5270821	463832249	9	~1987
5271179	42169433	8	~1985
5271319	52713191	8	~1985
5271323	137054399	9	~1986
5271401	42171209	8	~1985
5271463	52714631	8	~1985
5271557	158146711	9	~1986
5271599	10543199	8	~1983
5271743	10543487	8	~1983
5272103	10544207	8	~1983
5272237	84355793	8	~1986
5272411	84358577	8	~1986
5272583	10545167	8	~1983
5272649	42181193	8	~1985
5272739	390182687	9	~1987
5272807	84364913	8	~1986
5272979	10545959	8	~1983
5273087	42184697	8	~1985
5273123	10546247	8	~1983
5273531	10547063	8	~1983
5273537	42188297	8	~1985
5273711	10547423	8	~1983
5273759	10547519	8	~1983
5273759	126570217	9

Exp.	Prime Factor	Digits	Year
5273861	31643167	8	~1985
5274007	52740071	8	~1985
5274023	10548047	8	~1983
5274047	42192377	8	~1985
5274127	84386033	8	~1986
5274257	31645543	8	~1985
5274299	10548599	8	~1983
5274463	52744631	8	~1985
5274623	10549247	8	~1983
5274629	42197033	8	~1985
5274917	31649503	8	~1985
5275021	31650127	8	~1985
5275079	10550159	8	~1983
5275271	10550543	8	~1983
5275561	31653367	8	~1985
5275759	52757591	8	~1985
5275841	31655047	8	~1985
5276767	94981807	8	~1986
5276833	31660999	8	~1985
5277059	10554119	8	~1983
5277059	94987063	8
5277119	10554239	8	~1983
5277179	10554359	8	~1983
5277499	94994983	8	~1986
5277919	52779191	8	~1985

Exp.	Prime Factor	Digits	Year
5277983	10555967	8	~1983
5278033	31668199	8	~1985
5278139	10556279	8	~1983
5278541	31671247	8	~1985
5278571	42228569	8	~1985
5278877	31673263	8	~1985
5278913	31673479	8	~1985
5278991	10557983	8	~1983
5279003	10558007	8	~1983
5279243	10558487	8	~1983
5279501	31677007	8	~1985
5279531	10559063	8	~1983
5279621	42236969	8	~1985
5279767	52797671	8	~1985
5279873	31679239	8	~1985
5279909	42239273	8	~1985
5280239	10560479	8	~1983
5280263	10560527	8	~1983
5280371	10560743	8	~1983
5280437	42243497	8	~1985
5280449	126730777	9	~1986
5280481	31682887	8	~1985
5280553	116172167	9	~1986
5280791	10561583	8	~1983
5280809	42246473	8	~1985

Exp.	Prime Factor	Digits	Year
5281139	126747337	9	~1986
5281151	10562303	8	~1983
5281403	10562807	8	~1983
5281499	10562999	8	~1983
5281511	10563023	8	~1983
5281657	31689943	8	~1985
5281937	42255497	8	~1985
5282141	31692847	8	~1985
5282159	10564319	8	~1983
5282273	31693639	8	~1985
5282339	10564679	8	~1983
5282363	10564727	8	~1983
5282531	10565063	8	~1983
5282737	158482111	9	~1986
5282821	31696927	8	~1985
5282831	10565663	8	~1983
5282999	10565999	8	~1983
5283143	10566287	8	~1983
5283401	31700407	8	~1985
5283647	42269177	8	~1985
5283683	10567367	8	~1983
5283851	10567703	8	~1983
5284091	10568183	8	~1983
5284537	31707223	8	~1985
5284681	31708087	8	~1985

4.724.182 digits

25-04-13