Small Mersenne Prime Factors (page 961/5610)

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
8501201	51007207	8	~1986
8501239	85012391	8	~1987
8501243	17002487	8	~1985
8501443	340057721	9	~1988
8501459	17002919	8	~1985
8502181	51013087	8	~1986
8502311	17004623	8	~1985
8502503	17005007	8	~1985
8502883	85028831	8	~1987
8503091	17006183	8	~1985
8503223	221083799	9	~1988
8503403	17006807	8	~1985
8503427	153061687	9	~1987
8503499	17006999	8	~1985
8503501	51021007	8	~1986
8503513	51021079	8	~1986
8503751	17007503	8	~1985
8503871	68030969	8	~1987
8503919	17007839	8	~1985
8503991	153071839	9	~1987
8504129	68033033	8	~1987
8504203	85042031	8	~1987
8504357	119060999	9	~1987
8504591	17009183	8	~1985
8505037	51030223	8	~1986

Exp.	Prime Factor	Digits	Year
8505053	51030319	8	~1986
8505197	68041577	8	~1987
8505313	51031879	8	~1986
8505467	68043737	8	~1987
8505719	17011439	8	~1985
8505989	68047913	8	~1987
8506031	17012063	8	~1985
8506081	51036487	8	~1986
8506427	476359913	9	~1989
8506507	289221239	9	~1988
8506643	17013287	8	~1985
8506703	17013407	8	~1985
8506811	68054489	8	~1987
8506907	408331537	9	~1988
8507099	17014199	8	~1985
8507221	51043327	8	~1986
8507281	51043687	8	~1986
8507357	51044143	8	~1986
8507363	17014727	8	~1985
8507591	612546553	9	~1989
8507651	17015303	8	~1985
8507711	68061689	8	~1987
8507791	136124657	9	~1987
8508011	17016023	8	~1985
8508061	51048367	8	~1986

Exp.	Prime Factor	Digits	Year
8508191	17016383	8	~1985
8508373	51050239	8	~1986
8508757	51052543	8	~1986
8509079	17018159	8	~1985
8509121	68072969	8	~1987
8509147	85091471	8	~1987
8509211	17018423	8	~1985
8509247	68073977	8	~1987
8509331	17018663	8	~1985
8509433	119132063	9	~1987
8509601	51057607	8	~1986
8509619	17019239	8	~1985
8509661	255289831	9	~1988
8509799	17019599	8	~1985
8509861	51059167	8	~1986
8510039	17020079	8	~1985
8510441	68083529	8	~1987
8511001	51066007	8	~1986
8511131	17022263	8	~1985
8511367	1361818721	10	~1990
8511491	17022983	8	~1985
8511497	68091977	8	~1987
8511617	51069703	8	~1986
8511619	85116191	8	~1987
8511731	17023463	8	~1985

Exp.	Prime Factor	Digits	Year
8511803	17023607	8	~1985
8511821	51070927	8	~1986
8511913	51071479	8	~1986
8512111	136193777	9	~1987
8512351	136197617	9	~1987
8512391	17024783	8	~1985
8512391	153223039	9
8512453	51074719	8	~1986
8512547	68100377	8	~1987
8512643	17025287	8	~1985
8512799	17025599	8	~1985
8512883	476721449	9	~1989
8513033	51078199	8	~1986
8513171	17026343	8	~1985
8513207	153237727	9	~1987
8513291	68106329	8	~1987
8513341	51080047	8	~1986
8513497	51080983	8	~1986
8514173	51085039	8	~1986
8514179	17028359	8	~1985
8514277	408685297	9	~1989
8514419	68115353	8	~1987
8514509	68116073	8	~1987
8514743	17029487	8	~1985
8514949	187328879	9	~1988

5.307.017 digits

26-01-11