Small Mersenne Prime Factors (page 931/5550)

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
8112911	16225823	8	~1985
8113271	16226543	8	~1985
8113297	48679783	8	~1986
8113321	48679927	8	~1986
8113559	16227119	8	~1985
8113643	16227287	8	~1985
8113753	48682519	8	~1986
8113993	48683959	8	~1986
8114039	64912313	8	~1986
8114263	81142631	8	~1987
8114291	64914329	8	~1986
8114531	16229063	8	~1985
8114759	16229519	8	~1985
8114783	16229567	8	~1985
8114819	16229639	8	~1985
8115011	16230023	8	~1985
8115203	16230407	8	~1985
8115313	48691879	8	~1986
8115539	16231079	8	~1985
8115671	64925369	8	~1986
8116133	48696799	8	~1986
8116307	64930457	8	~1986
8116421	48698527	8	~1986
8116441	48698647	8	~1986
8116741	48700447	8	~1986

Exp.	Prime Factor	Digits	Year
8116799	16233599	8	~1985
8117243	16234487	8	~1985
8117521	48705127	8	~1986
8117933	48707599	8	~1986
8117951	16235903	8	~1985
8118023	16236047	8	~1985
8118083	16236167	8	~1985
8118137	48708823	8	~1986
8118191	16236383	8	~1985
8118233	48709399	8	~1986
8118251	16236503	8	~1985
8118413	48710479	8	~1986
8118589	194846137	9	~1988
8118611	16237223	8	~1985
8119151	16238303	8	~1985
8119211	16238423	8	~1985
8119313	48715879	8	~1986
8119337	48716023	8	~1986
8119361	48716167	8	~1986
8119439	16238879	8	~1985
8119451	16238903	8	~1985
8119637	64957097	8	~1986
8119697	113675759	9	~1987
8120117	48720703	8	~1986
8120243	16240487	8	~1985

Exp.	Prime Factor	Digits	Year
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
8123657	48741943	8	~1986

Exp.	Prime Factor	Digits	Year
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
8126711	16253423	8	~1985

5.247.179 digits

25-12-14