Small Mersenne Prime Factors (page 696/5025)

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
5233271	94198879	8	~1986
5233381	83734097	8	~1986
5233439	10466879	8	~1983
5233619	10467239	8	~1983
5233649	41869193	8	~1985
5233751	41870009	8	~1985
5233793	31402759	8	~1985
5233997	73275959	8	~1986
5234111	10468223	8	~1983
5234399	41875193	8	~1985
5234483	10468967	8	~1983
5234491	94220839	8	~1986
5234513	73283183	8	~1986
5234741	41877929	8	~1985
5234843	10469687	8	~1983
5234917	31409503	8	~1985
5235281	31411687	8	~1985
5235437	41883497	8	~1985
5235481	209419241	9	~1987
5235539	10471079	8	~1983
5235613	17801084201	11	~1991
5235673	31414039	8	~1985
5235673	376968457	9
5235761	31414567	8	~1985
5235803	10471607	8	~1983

Exp.	Prime Factor	Digits	Year
5236093	31416559	8	~1985
5236139	10472279	8	~1983
5236193	31417159	8	~1985
5236261	31417567	8	~1985
5236271	10472543	8	~1983
5236271	41890169	8
5236447	83783153	8	~1986
5236661	31419967	8	~1985
5237579	10475159	8	~1983
5238143	10476287	8	~1983
5238179	10476359	8	~1983
5238203	10476407	8	~1983
5238251	10476503	8	~1983
5238323	10476647	8	~1983
5238419	10476839	8	~1983
5238671	10477343	8	~1983
5238731	10477463	8	~1983
5238911	10477823	8	~1983
5238929	41911433	8	~1985
5239033	31434199	8	~1985
5239181	31435087	8	~1985
5239271	10478543	8	~1983
5239393	31436359	8	~1985
5239447	52394471	8	~1985
5239627	83834033	8	~1986

Exp.	Prime Factor	Digits	Year
5239931	10479863	8	~1983
5240093	660251719	9	~1988
5240099	10480199	8	~1983
5240107	125762569	9	~1986
5240177	157205311	9	~1986
5240303	10480607	8	~1983
5240357	41922857	8	~1985
5240377	31442263	8	~1985
5240383	83846129	8	~1986
5240413	31442479	8	~1985
5240783	10481567	8	~1983
5240819	41926553	8	~1985
5240897	157226911	9	~1986
5240951	10481903	8	~1983
5241101	31446607	8	~1985
5241521	31449127	8	~1985
5241667	52416671	8	~1985
5241959	10483919	8	~1983
5242067	41936537	8	~1985
5242201	31453207	8	~1985
5242217	41937737	8	~1985
5242313	31453879	8	~1985
5242439	10484879	8	~1983
5242561	31455367	8	~1985
5242571	10485143	8	~1983

Exp.	Prime Factor	Digits	Year
5242577	73396079	8	~1986
5242619	10485239	8	~1983
5242703	10485407	8	~1983
5242877	73400279	8	~1986
5242883	10485767	8	~1983
5243023	83888369	8	~1986
5243081	31458487	8	~1985
5243339	41946713	8	~1985
5243479	52434791	8	~1985
5243501	41948009	8	~1985
5243521	31461127	8	~1985
5243993	31463959	8	~1985
5244013	31464079	8	~1985
5244277	31465663	8	~1985
5244311	10488623	8	~1983
5244641	31467847	8	~1985
5244641	293699897	9
5244661	31467967	8	~1985
5244671	10489343	8	~1983
5244803	10489607	8	~1983
5244937	157348111	9	~1986
5245139	41961113	8	~1985
5245397	125889529	9	~1986
5245619	41964953	8	~1985
5246089	115413959	9	~1986

4.724.182 digits

25-04-13