Small Mersenne Prime Factors (page 912/5205)

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
8120243	16240487	8	~1985
8120317	48721903	8	~1986
8120459	16240919	8	~1985
8120597	113688359	9	~1987
8120617	519719489	9	~1989
8120659	146171863	9	~1987
8120741	48724447	8	~1986
8120789	64966313	8	~1986
8121401	64971209	8	~1986
8121419	16242839	8	~1985
8121433	48728599	8	~1986
8121629	64973033	8	~1986
8121671	16243343	8	~1985
8121851	64974809	8	~1986
8121959	16243919	8	~1985
8122021	48732127	8	~1986
8122043	16244087	8	~1985
8122157	194931769	9	~1988
8122757	48736543	8	~1986
8122799	16245599	8	~1985
8123197	243695911	9	~1988
8123471	16246943	8	~1985
8123477	64987817	8	~1986
8123593	48741559	8	~1986
8123593	129977489	9

Exp.	Prime Factor	Digits	Year
8123657	48741943	8	~1986
8123873	48743239	8	~1986
8123897	308708087	9	~1988
8124023	16248047	8	~1985
8124247	194981929	9	~1988
8124323	16248647	8	~1985
8124341	64994729	8	~1986
8124491	16248983	8	~1985
8124503	16249007	8	~1985
8124659	16249319	8	~1985
8124731	16249463	8	~1985
8124839	16249679	8	~1985
8124877	48749263	8	~1986
8124923	16249847	8	~1985
8125177	130002833	9	~1987
8125223	16250447	8	~1985
8125319	16250639	8	~1985
8125343	16250687	8	~1985
8125639	715056233	9	~1989
8125811	16251623	8	~1985
8125823	16251647	8	~1985
8126009	390048433	9	~1988
8126087	406304351	9	~1988
8126137	195027289	9	~1988
8126213	48757279	8	~1986

Exp.	Prime Factor	Digits	Year
8126711	16253423	8	~1985
8126879	65015033	8	~1986
8127023	16254047	8	~1985
8127083	16254167	8	~1985
8127233	48763399	8	~1986
8127271	130036337	9	~1987
8127293	113782103	9	~1987
8127313	48763879	8	~1986
8127551	16255103	8	~1985
8127923	16255847	8	~1985
8129081	48774487	8	~1986
8129123	16258247	8	~1985
8129221	390202609	9	~1988
8129339	65034713	8	~1986
8129411	536541127	9	~1989
8129413	48776479	8	~1986
8129477	48776863	8	~1986
8129507	65036057	8	~1986
8129783	16259567	8	~1985
8129939	16259879	8	~1985
8130581	65044649	8	~1986
8130599	195134377	9	~1988
8130673	130090769	9	~1987
8130851	16261703	8	~1985
8130911	16261823	8	~1985

Exp.	Prime Factor	Digits	Year
8131241	48787447	8	~1986
8131337	48788023	8	~1986
8131633	48789799	8	~1986
8131961	48791767	8	~1986
8132051	16264103	8	~1985
8132219	16264439	8	~1985
8132291	16264583	8	~1985
8132347	130117553	9	~1987
8132483	16264967	8	~1985
8132759	16265519	8	~1985
8132843	16265687	8	~1985
8133241	130131857	9	~1987
8133371	16266743	8	~1985
8133403	81334031	8	~1987
8133791	16267583	8	~1985
8133971	16267943	8	~1985
8134739	16269479	8	~1985
8134799	16269599	8	~1985
8134949	65079593	8	~1986
8135201	48811207	8	~1986
8135221	48811327	8	~1986
8135243	16270487	8	~1985
8135279	16270559	8	~1985
8135279	65082233	8
8135581	48813487	8	~1986

4.903.097 digits

25-07-08