Small Mersenne Prime Factors (page 898/5670)

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
7525151	60201209	8	~1986
7525403	15050807	8	~1985
7525571	15051143	8	~1985
7525601	45153607	8	~1986
7525657	120410513	9	~1987
7525943	15051887	8	~1985
7526297	60210377	8	~1986
7526447	60211577	8	~1986
7526663	15053327	8	~1985
7526993	45161959	8	~1986
7527181	45163087	8	~1986
7527419	677467711	9	~1989
7528043	15056087	8	~1985
7528091	15056183	8	~1985
7528111	75281111	8	~1986
7528357	11563556353	11	~1992
7528393	165624647	9	~1987
7528403	15056807	8	~1985
7528537	45171223	8	~1986
7529099	240931169	9	~1988
7529261	60234089	8	~1986
7529771	15059543	8	~1985
7529783	15059567	8	~1985
7529831	15059663	8	~1985
7529857	45179143	8	~1986

Exp.	Prime Factor	Digits	Year
7529881	45179287	8	~1986
7529903	240956897	9	~1988
7529939	15059879	8	~1985
7530073	45180439	8	~1986
7530121	165662663	9	~1987
7530239	361451473	9	~1988
7530353	45182119	8	~1986
7530569	240978209	9	~1988
7530791	15061583	8	~1985
7530851	15061703	8	~1985
7531019	15062039	8	~1985
7531157	60249257	8	~1986
7531423	180754153	9	~1987
7531451	15062903	8	~1985
7531871	15063743	8	~1985
7532507	195845183	9	~1987
7532537	60260297	8	~1986
7532579	15065159	8	~1985
7532771	15065543	8	~1985
7532773	45196639	8	~1986
7533131	15066263	8	~1985
7533181	45199087	8	~1986
7533199	482124737	9	~1988
7533221	60265769	8	~1986
7533571	135604279	9	~1987

Exp.	Prime Factor	Digits	Year
7533611	15067223	8	~1985
7533731	15067463	8	~1985
7533751	75337511	8	~1986
7533781	45202687	8	~1986
7533859	180812617	9	~1987
7533947	60271577	8	~1986
7534367	60274937	8	~1986
7534463	15068927	8	~1985
7534511	15069023	8	~1985
7534817	45208903	8	~1986
7535167	135633007	9	~1987
7535243	15070487	8	~1985
7535417	60283337	8	~1986
7535459	15070919	8	~1985
7535519	60284153	8	~1986
7535701	45214207	8	~1986
7535771	60286169	8	~1986
7536031	120576497	9	~1987
7536443	15072887	8	~1985
7537037	648185183	9	~1989
7537067	5381465839	10	~1991
7537331	15074663	8	~1985
7537559	15075119	8	~1985
7537703	15075407	8	~1985
7537763	15075527	8	~1985

Exp.	Prime Factor	Digits	Year
7537861	45227167	8	~1986
7538093	45228559	8	~1986
7538423	15076847	8	~1985
7538501	45231007	8	~1986
7538519	15077039	8	~1985
7538543	15077087	8	~1985
7538759	15077519	8	~1985
7538849	60310793	8	~1986
7539089	180938137	9	~1987
7539341	60314729	8	~1986
7539397	45236383	8	~1986
7539743	15079487	8	~1985
7539919	135718543	9	~1987
7540199	15080399	8	~1985
7540237	180965689	9	~1987
7540451	15080903	8	~1985
7540499	15080999	8	~1985
7540517	904862041	9	~1989
7540751	15081503	8	~1985
7540751	60326009	8
7540763	15081527	8	~1985
7540769	226223071	9	~1988
7540997	45245983	8	~1986
7540997	60327977	8
7541057	45246343	8	~1986

5.366.787 digits

26-02-08