Small Mersenne Prime Factors (page 967/5460)

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
8721913	52331479	8	~1986
8722097	52332583	8	~1986
8722211	69777689	8	~1987
8722409	69779273	8	~1987
8722607	69780857	8	~1987
8722799	17445599	8	~1985
8722859	69782873	8	~1987
8723063	17446127	8	~1985
8723213	52339279	8	~1986
8723321	69786569	8	~1987
8723441	52340647	8	~1986
8723459	69787673	8	~1987
8723531	17447063	8	~1985
8723789	69790313	8	~1987
8723993	52343959	8	~1986
8724143	17448287	8	~1985
8724479	69795833	8	~1987
8724641	52347847	8	~1986
8724721	52348327	8	~1986
8725091	17450183	8	~1985
8725177	52351063	8	~1986
8725217	52351303	8	~1986
8725217	69801737	8
8725421	69803369	8	~1987
8725489	209411737	9	~1988

Exp.	Prime Factor	Digits	Year
8725511	17451023	8	~1985
8725621	261768631	9	~1988
8725631	17451263	8	~1985
8725823	17451647	8	~1985
8726351	17452703	8	~1985
8727053	52362319	8	~1986
8727161	69817289	8	~1987
8727263	17454527	8	~1985
8727343	139637489	9	~1987
8728303	296762303	9	~1988
8728427	157111687	9	~1988
8728679	17457359	8	~1985
8728757	52372543	8	~1986
8728823	17457647	8	~1985
8728969	192037319	9	~1988
8729183	17458367	8	~1985
8729291	17458583	8	~1985
8729317	52375903	8	~1986
8729411	17458823	8	~1985
8729429	69835433	8	~1987
8729543	17459087	8	~1985
8729711	69837689	8	~1987
8729821	52378927	8	~1986
8730083	17460167	8	~1985
8730331	139685297	9	~1987

Exp.	Prime Factor	Digits	Year
8730983	17461967	8	~1985
8731031	17462063	8	~1985
8731139	69849113	8	~1987
8731531	87315311	8	~1987
8731939	87319391	8	~1987
8731939	157174903	9
8732051	17464103	8	~1985
8732093	52392559	8	~1986
8732201	52393207	8	~1986
8732261	52393567	8	~1986
8732351	69858809	8	~1987
8732489	69859913	8	~1987
8732653	52395919	8	~1986
8732819	17465639	8	~1985
8732819	69862553	8
8732879	17465759	8	~1985
8733083	17466167	8	~1985
8733251	17466503	8	~1985
8733259	349330361	9	~1988
8733541	52401247	8	~1986
8733547	768552137	9	~1989
8733551	17467103	8	~1985
8733743	17467487	8	~1985
8733839	17467679	8	~1985
8734223	17468447	8	~1985

Exp.	Prime Factor	Digits	Year
8734841	52409047	8	~1986
8734919	17469839	8	~1985
8735341	262060231	9	~1988
8735429	69883433	8	~1987
8735621	52413727	8	~1986
8735711	17471423	8	~1985
8735849	69886793	8	~1987
8736179	17472359	8	~1985
8736263	17472527	8	~1985
8736659	17473319	8	~1985
8736719	17473439	8	~1985
8737139	17474279	8	~1985
8737271	17474543	8	~1985
8737357	52424143	8	~1986
8737483	87374831	8	~1987
8737763	17475527	8	~1985
8737829	69902633	8	~1987
8737979	17475959	8	~1985
8738033	279617057	9	~1988
8738231	17476463	8	~1985
8738351	17476703	8	~1985
8738363	17476727	8	~1985
8738377	52430263	8	~1986
8738591	17477183	8	~1985
8738711	17477423	8	~1985

5.157.210 digits

25-11-02