Small Mersenne Prime Factors (page 993/5730)

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
8888461	995507633	9	~1990
8888531	17777063	8	~1985
8888651	17777303	8	~1985
8889427	160009687	9	~1988
8889659	17779319	8	~1985
8889719	17779439	8	~1985
8889757	53338543	8	~1986
8889821	497829977	9	~1989
8889851	17779703	8	~1985
8889851	71118809	8
8890073	53340439	8	~1986
8890243	88902431	8	~1987
8890457	53342743	8	~1986
8890513	53343079	8	~1986
8890621	53343727	8	~1986
8890709	71125673	8	~1987
8891171	17782343	8	~1985
8891237	53347423	8	~1986
8891471	17782943	8	~1985
8891549	71132393	8	~1987
8891557	53349343	8	~1986
8891579	17783159	8	~1985
8891843	17783687	8	~1985
8891999	17783999	8	~1985
8892077	53352463	8	~1986

Exp.	Prime Factor	Digits	Year
8892217	622455191	9	~1989
8892263	17784527	8	~1985
8892431	17784863	8	~1985
8892491	17784983	8	~1985
8892553	53355319	8	~1986
8892607	160066927	9	~1988
8892857	71142857	8	~1987
8893177	53359063	8	~1986
8893259	17786519	8	~1985
8893331	17786663	8	~1985
8893799	17787599	8	~1985
8893897	53363383	8	~1986
8894003	17788007	8	~1985
8894351	17788703	8	~1985
8894377	53366263	8	~1986
8894423	17788847	8	~1985
8894657	53367943	8	~1986
8894843	17789687	8	~1985
8895179	17790359	8	~1985
8895221	53371327	8	~1986
8895223	88952231	8	~1987
8895251	17790503	8	~1985
8895311	17790623	8	~1985
8895611	17791223	8	~1985
8895959	17791919	8	~1985

Exp.	Prime Factor	Digits	Year
8896259	17792519	8	~1985
8896801	53380807	8	~1986
8896931	17793863	8	~1985
8897183	17794367	8	~1985
8897221	53383327	8	~1986
8897621	71180969	8	~1987
8897771	17795543	8	~1985
8897773	53386639	8	~1986
8897831	17795663	8	~1985
8897857	53387143	8	~1986
8898301	53389807	8	~1986
8898551	17797103	8	~1985
8898671	17797343	8	~1985
8898733	53392399	8	~1986
8898971	17797943	8	~1985
8898977	71191817	8	~1987
8899031	17798063	8	~1985
8899031	71192249	8
8899181	71193449	8	~1987
8899193	53395159	8	~1986
8899417	53396503	8	~1986
8899711	142395377	9	~1987
8899837	266995111	9	~1988
8899853	53399119	8	~1986
8899867	88998671	8	~1987

Exp.	Prime Factor	Digits	Year
8899937	53399623	8	~1986
8899997	71199977	8	~1987
8900123	1014614023	10	~1990
8900201	53401207	8	~1986
8900273	124603823	9	~1987
8900279	71202233	8	~1987
8900399	17800799	8	~1985
8900669	213616057	9	~1988
8900891	17801783	8	~1985
8900929	195820439	9	~1988
8901121	195824663	9	~1988
8901467	71211737	8	~1987
8901881	71215049	8	~1987
8901911	17803823	8	~1985
8901911	71215289	8
8901923	17803847	8	~1985
8902037	53412223	8	~1986
8902211	71217689	8	~1987
8902499	17804999	8	~1985
8902717	53416303	8	~1986
8902871	17805743	8	~1985
8902871	71222969	8
8903183	17806367	8	~1985
8903201	53419207	8	~1986
8903759	17807519	8	~1985

5.426.516 digits

26-03-08