Small Mersenne Prime Factors (page 934/5460)

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
8229191	16458383	8	~1985
8229283	82292831	8	~1987
8229323	16458647	8	~1985
8229619	4427535023	10	~1991
8230121	65840969	8	~1986
8230471	82304711	8	~1987
8230583	16461167	8	~1985
8230799	65846393	8	~1986
8231219	197549257	9	~1988
8231231	16462463	8	~1985
8231291	16462583	8	~1985
8231297	65850377	8	~1986
8231423	16462847	8	~1985
8231437	49388623	8	~1986
8231933	197566393	9	~1988
8232109	181106399	9	~1988
8232121	49392727	8	~1986
8232151	82321511	8	~1987
8232179	16464359	8	~1985
8232197	65857577	8	~1986
8232359	395153233	9	~1988
8232373	49394239	8	~1986
8232527	65860217	8	~1986
8232557	49395343	8	~1986
8233031	16466063	8	~1985

Exp.	Prime Factor	Digits	Year
8233033	49398199	8	~1986
8233163	16466327	8	~1985
8233171	10274997409	11	~1992
8233367	65866937	8	~1986
8233453	49400719	8	~1986
8233679	16467359	8	~1985
8233937	49403623	8	~1986
8233949	444633247	9	~1989
8234123	16468247	8	~1985
8234141	49404847	8	~1986
8234279	16468559	8	~1985
8234321	65874569	8	~1986
8234711	16469423	8	~1985
8234921	49409527	8	~1986
8235323	16470647	8	~1985
8235371	65882969	8	~1986
8235433	49412599	8	~1986
8235791	16471583	8	~1985
8235881	65887049	8	~1986
8236031	16472063	8	~1985
8236057	49416343	8	~1986
8236103	16472207	8	~1985
8236133	49416799	8	~1986
8236181	65889449	8	~1986
8236271	65890169	8	~1986

Exp.	Prime Factor	Digits	Year
8236337	49418023	8	~1986
8236379	16472759	8	~1985
8236451	16472903	8	~1985
8236499	65891993	8	~1986
8236583	16473167	8	~1985
8236589	65892713	8	~1986
8236637	49419823	8	~1986
8236801	49420807	8	~1986
8236883	16473767	8	~1985
8237063	16474127	8	~1985
8237137	49422823	8	~1986
8237303	16474607	8	~1985
8237417	49424503	8	~1986
8237497	49424983	8	~1986
8237699	65901593	8	~1986
8238011	65904089	8	~1986
8238371	65906969	8	~1986
8238493	181246847	9	~1988
8239019	16478039	8	~1985
8239151	16478303	8	~1985
8239513	49437079	8	~1986
8239571	16479143	8	~1985
8239631	16479263	8	~1985
8239879	82398791	8	~1987
8240339	16480679	8	~1985

Exp.	Prime Factor	Digits	Year
8240621	49443727	8	~1986
8240663	16481327	8	~1985
8240753	49444519	8	~1986
8240759	16481519	8	~1985
8241131	65929049	8	~1986
8241131	148340359	9
8241143	197787433	9	~1988
8241601	49449607	8	~1986
8241901	49451407	8	~1986
8241911	16483823	8	~1985
8241931	131870897	9	~1987
8242109	65936873	8	~1986
8242361	65938889	8	~1986
8242571	16485143	8	~1985
8242631	16485263	8	~1985
8242877	115400279	9	~1987
8242933	49457599	8	~1986
8243099	16486199	8	~1985
8243681	49462087	8	~1986
8244083	16488167	8	~1985
8244191	16488383	8	~1985
8244611	16489223	8	~1985
8244757	49468543	8	~1986
8244911	346286263	9	~1988
8244989	65959913	8	~1986

5.157.210 digits

25-11-02