Small Mersenne Prime Factors (page 732/6045)

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
5170463	10340927	8	~1983
5170519	51705191	8	~1985
5170559	93070063	8	~1986
5170577	72388079	8	~1986
5170673	165461537	9	~1986
5170727	93073087	8	~1986
5170751	10341503	8	~1983
5171123	382663103	9	~1987
5171129	124107097	9	~1986
5171279	41370233	8	~1985
5171381	41371049	8	~1985
5171461	82743377	8	~1986
5171753	72404543	8	~1986
5171801	31030807	8	~1985
5171839	124124137	9	~1986
5171843	10343687	8	~1983
5171951	10343903	8	~1983
5172017	72408239	8	~1986
5172073	82753169	8	~1986
5172221	41377769	8	~1985
5172239	10344479	8	~1983
5172287	41378297	8	~1985
5172383	10344767	8	~1983
5172407	41379257	8	~1985
5172457	31034743	8	~1985

Exp.	Prime Factor	Digits	Year
5172553	82760849	8	~1986
5172571	51725711	8	~1985
5172659	10345319	8	~1983
5172851	10345703	8	~1983
5172899	10345799	8	~1983
5173193	31039159	8	~1985
5173211	10346423	8	~1983
5173241	31039447	8	~1985
5173319	10346639	8	~1983
5173331	10346663	8	~1983
5173829	41390633	8	~1985
5173859	10347719	8	~1983
5174003	10348007	8	~1983
5174047	51740471	8	~1985
5174219	10348439	8	~1983
5174243	10348487	8	~1983
5174399	10348799	8	~1983
5174419	51744191	8	~1985
5174423	10348847	8	~1983
5174461	31046767	8	~1985
5174473	31046839	8	~1985
5174531	10349063	8	~1983
5174887	124197289	9	~1986
5174959	51749591	8	~1985
5175019	124200457	9	~1986

Exp.	Prime Factor	Digits	Year
5175041	31050247	8	~1985
5175251	10350503	8	~1983
5175323	10350647	8	~1983
5175433	331227713	9	~1987
5175509	527901919	9	~1988
5175557	41404457	8	~1985
5175721	207028841	9	~1987
5175727	124217449	9	~1986
5175839	93165103	8	~1986
5176091	10352183	8	~1983
5176187	41409497	8	~1985
5176387	51763871	8	~1985
5176511	10353023	8	~1983
5176631	10353263	8	~1983
5176667	93180007	8	~1986
5177059	51770591	8	~1985
5177119	176022047	9	~1986
5177203	176024903	9	~1986
5177351	10354703	8	~1983
5177363	10354727	8	~1983
5177441	41419529	8	~1985
5177477	31064863	8	~1985
5177551	93195919	8	~1986
5177701	31066207	8	~1985
5177971	51779711	8	~1985

Exp.	Prime Factor	Digits	Year
5177971	93203479	8
5178083	10356167	8	~1983
5178143	10356287	8	~1983
5178661	31071967	8	~1985
5178923	10357847	8	~1983
5179103	10358207	8	~1983
5179649	72515087	8	~1986
5179859	10359719	8	~1983
5180137	31080823	8	~1985
5180159	10360319	8	~1983
5180237	124325689	9	~1986
5180243	10360487	8	~1983
5180341	31082047	8	~1985
5180459	10360919	8	~1983
5180477	72526679	8	~1986
5180579	10361159	8	~1983
5180717	31084303	8	~1985
5180717	41445737	8
5180771	10361543	8	~1983
5180953	155428591	9	~1986
5180963	10361927	8	~1983
5181013	31086079	8	~1985
5181023	10362047	8	~1983
5181067	93259207	8	~1986
5181101	31086607	8	~1985

5.740.663 digits

26-08-02