Small Mersenne Prime Factors (page 723/5670)

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
5226983	10453967	8	~1983
5227073	31362439	8	~1985
5227283	10454567	8	~1983
5227501	31365007	8	~1985
5227507	52275071	8	~1985
5227591	83641457	8	~1986
5227769	41822153	8	~1985
5227769	73188767	8
5228159	10456319	8	~1983
5228263	52282631	8	~1985
5228339	10456679	8	~1983
5228437	491473079	9	~1988
5228453	73198343	8	~1986
5228473	31370839	8	~1985
5228539	52285391	8	~1985
5228651	10457303	8	~1983
5228761	31372567	8	~1985
5228777	73202879	8	~1986
5228921	198698999	9	~1987
5228963	135953039	9	~1986
5228969	41831753	8	~1985
5229071	10458143	8	~1983
5229151	52291511	8	~1985
5229299	10458599	8	~1983
5229377	31376263	8	~1985

Exp.	Prime Factor	Digits	Year
5229391	52293911	8	~1985
5229443	10458887	8	~1983
5229491	10458983	8	~1983
5229569	167346209	9	~1986
5229661	31377967	8	~1985
5229857	41838857	8	~1985
5229911	94138399	8	~1986
5229943	52299431	8	~1985
5230021	31380127	8	~1985
5230193	31381159	8	~1985
5230259	10460519	8	~1983
5230397	41843177	8	~1985
5230399	52303991	8	~1985
5230691	10461383	8	~1983
5230837	31385023	8	~1985
5230921	31385527	8	~1985
5230997	73233959	8	~1986
5231029	209241161	9	~1987
5231111	10462223	8	~1983
5231311	52313111	8	~1985
5231411	219719263	9	~1987
5231483	10462967	8	~1983
5231701	31390207	8	~1985
5231827	52318271	8	~1985
5232559	52325591	8	~1985

Exp.	Prime Factor	Digits	Year
5232761	41862089	8	~1985
5232977	41863817	8	~1985
5233043	10466087	8	~1983
5233133	31398799	8	~1985
5233139	10466279	8	~1983
5233223	10466447	8	~1983
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

Exp.	Prime Factor	Digits	Year
5235539	10471079	8	~1983
5235613	17801084201	11	~1991
5235673	31414039	8	~1985
5235673	376968457	9
5235761	31414567	8	~1985
5235803	10471607	8	~1983
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
5236631	136152407	9	~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

5.366.787 digits

26-02-08