Small Mersenne Prime Factors (page 735/5865)

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
5281937	42255497	8	~1985
5282141	31692847	8	~1985
5282159	10564319	8	~1984
5282273	31693639	8	~1985
5282339	10564679	8	~1984
5282363	10564727	8	~1984
5282531	10565063	8	~1984
5282737	158482111	9	~1986
5282821	31696927	8	~1985
5282831	10565663	8	~1984
5282999	10565999	8	~1984
5283143	10566287	8	~1984
5283401	31700407	8	~1985
5283647	42269177	8	~1985
5283683	10567367	8	~1984
5283851	10567703	8	~1984
5284091	10568183	8	~1984
5284537	31707223	8	~1985
5284681	31708087	8	~1985
5284751	42278009	8	~1985
5284987	52849871	8	~1985
5285129	42281033	8	~1985
5285183	10570367	8	~1984
5285219	42281753	8	~1985
5285237	31711423	8	~1985

Exp.	Prime Factor	Digits	Year
5285587	84569393	8	~1986
5285659	52856591	8	~1985
5285677	31714063	8	~1985
5286277	31717663	8	~1985
5286553	31719319	8	~1985
5286641	42293129	8	~1985
5286971	10573943	8	~1984
5287043	380667097	9	~1987
5287379	95172823	8	~1986
5287531	52875311	8	~1985
5287679	10575359	8	~1984
5287991	42303929	8	~1985
5288033	31728199	8	~1985
5288083	52880831	8	~1985
5288219	10576439	8	~1984
5288477	31730863	8	~1985
5288489	74038847	8	~1986
5288609	42308873	8	~1985
5288681	31732087	8	~1985
5288917	31733503	8	~1985
5288953	31733719	8	~1985
5289071	10578143	8	~1984
5289073	158672191	9	~1986
5289247	52892471	8	~1985
5289463	52894631	8	~1985

Exp.	Prime Factor	Digits	Year
5289503	10579007	8	~1984
5289611	42316889	8	~1985
5289659	10579319	8	~1984
5289743	10579487	8	~1984
5289841	253912369	9	~1987
5289883	560727599	9	~1988
5289913	126957913	9	~1986
5289913	5998761343	10
5290079	10580159	8	~1984
5290163	10580327	8	~1984
5290199	10580399	8	~1984
5290361	31742167	8	~1985
5290561	31743367	8	~1985
5290661	581972711	9	~1988
5290679	10581359	8	~1984
5290717	31744303	8	~1985
5290913	31745479	8	~1985
5290997	31745983	8	~1985
5291399	10582799	8	~1984
5291599	52915991	8	~1985
5291719	52917191	8	~1985
5291837	31751023	8	~1985
5291939	10583879	8	~1984
5292071	10584143	8	~1984
5292367	52923671	8	~1985

Exp.	Prime Factor	Digits	Year
5292641	42341129	8	~1985
5292671	10585343	8	~1984
5292809	42342473	8	~1985
5293291	52932911	8	~1985
5293439	10586879	8	~1984
5293619	42348953	8	~1985
5293621	31761727	8	~1985
5293643	137634719	9	~1986
5293679	10587359	8	~1984
5293709	42349673	8	~1985
5293829	74113607	8	~1986
5294111	10588223	8	~1984
5294231	10588463	8	~1984
5294489	158834671	9	~1986
5294543	10589087	8	~1984
5294543	296494409	9
5294587	95302567	8	~1986
5294717	42357737	8	~1985
5294759	10589519	8	~1984
5294771	10589543	8	~1984
5295239	10590479	8	~1984
5295343	222404407	9	~1987
5295431	10590863	8	~1984
5295527	137683703	9	~1986
5295599	10591199	8	~1984

5.561.074 digits

26-05-10