Small Mersenne Prime Factors (page 697/5460)

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
5007841	30047047	8	~1984
5008187	90147367	8	~1986
5008739	10017479	8	~1983
5008841	40070729	8	~1985
5009099	10018199	8	~1983
5009099	40072793	8
5009117	40072937	8	~1985
5009617	150288511	9	~1986
5009621	40076969	8	~1985
5009783	10019567	8	~1983
5009881	30059287	8	~1984
5009909	150297271	9	~1986
5009957	40079657	8	~1985
5010497	70146959	8	~1985
5010539	10021079	8	~1983
5010787	200431481	9	~1987
5011001	30066007	8	~1984
5011043	10022087	8	~1983
5011151	10022303	8	~1983
5011199	10022399	8	~1983
5011271	10022543	8	~1983
5011529	40092233	8	~1985
5011537	30069223	8	~1984
5011561	30069367	8	~1984
5011879	50118791	8	~1985

Exp.	Prime Factor	Digits	Year
5011927	50119271	8	~1985
5012053	30072319	8	~1984
5012177	40097417	8	~1985
5012377	30074263	8	~1984
5012377	240594097	9
5012383	601485961	9	~1988
5012417	30074503	8	~1984
5012507	40100057	8	~1985
5012521	30075127	8	~1984
5012653	110278367	9	~1986
5012831	10025663	8	~1983
5012939	10025879	8	~1983
5013089	190497383	9	~1986
5013119	10026239	8	~1983
5013139	50131391	8	~1985
5013191	10026383	8	~1983
5013301	30079807	8	~1984
5013527	90243487	8	~1986
5013647	40109177	8	~1985
5013719	10027439	8	~1983
5013779	10027559	8	~1983
5013797	30082783	8	~1984
5013961	200558441	9	~1987
5014199	10028399	8	~1983
5014561	30087367	8	~1984

Exp.	Prime Factor	Digits	Year
5014687	80234993	8	~1986
5014921	230686367	9	~1987
5014951	50149511	8	~1985
5014979	10029959	8	~1983
5015033	70210463	8	~1985
5015123	10030247	8	~1983
5015141	40121129	8	~1985
5015287	90275167	8	~1986
5015291	10030583	8	~1983
5015513	30093079	8	~1984
5015723	10031447	8	~1983
5015797	30094783	8	~1984
5015897	30095383	8	~1984
5016059	10032119	8	~1983
5016097	80257553	8	~1986
5016299	10032599	8	~1983
5016443	10032887	8	~1983
5016923	10033847	8	~1983
5016983	10033967	8	~1983
5017021	80272337	8	~1986
5017079	10034159	8	~1983
5017253	70241543	8	~1985
5017361	30104167	8	~1984
5017451	10034903	8	~1983
5017511	10035023	8	~1983

Exp.	Prime Factor	Digits	Year
5017583	10035167	8	~1983
5017721	30106327	8	~1984
5017889	2077406047	10	~1989
5018003	10036007	8	~1983
5018177	70254479	8	~1985
5018437	80294993	8	~1986
5018513	30111079	8	~1984
5018513	70259183	8
5018593	80297489	8	~1986
5018647	50186471	8	~1985
5018803	50188031	8	~1985
5018837	30113023	8	~1984
5018887	50188871	8	~1985
5018891	90340039	8	~1986
5019067	50190671	8	~1985
5019187	120460489	9	~1986
5019299	10038599	8	~1983
5019319	90347743	8	~1986
5019431	40155449	8	~1985
5019473	160623137	9	~1986
5019569	40156553	8	~1985
5019767	40158137	8	~1985
5019797	30118783	8	~1984
5020139	40161113	8	~1985
5020201	30121207	8	~1984

5.157.210 digits

25-11-02