Small Mersenne Prime Factors (page 971/5610)

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
8656379	17312759	8	~1985
8656481	69251849	8	~1987
8656691	17313383	8	~1985
8656919	17313839	8	~1985
8656979	69255833	8	~1987
8657021	51942127	8	~1986
8657333	51943999	8	~1986
8657639	207783337	9	~1988
8657651	17315303	8	~1985
8657723	17315447	8	~1985
8658193	51949159	8	~1986
8658323	17316647	8	~1985
8658383	484869449	9	~1989
8658659	17317319	8	~1985
8658673	51952039	8	~1986
8658829	259764871	9	~1988
8658893	51953359	8	~1986
8658893	623440297	9
8658983	17317967	8	~1985
8659153	3117295081	10	~1991
8659181	51955087	8	~1986
8659463	17318927	8	~1985
8660081	69280649	8	~1987
8660507	69284057	8	~1987
8660921	51965527	8	~1986

Exp.	Prime Factor	Digits	Year
8660983	138575729	9	~1987
8661047	69288377	8	~1987
8661173	51967039	8	~1986
8661197	51967183	8	~1986
8661509	69292073	8	~1987
8661553	51969319	8	~1986
8661581	69292649	8	~1987
8661703	86617031	8	~1987
8662019	17324039	8	~1985
8662133	51972799	8	~1986
8662151	17324303	8	~1985
8662169	69297353	8	~1987
8662481	51974887	8	~1986
8662531	155925559	9	~1988
8662799	17325599	8	~1985
8662859	433142951	9	~1989
8663437	51980623	8	~1986
8663519	17327039	8	~1985
8663579	17327159	8	~1985
8663777	69310217	8	~1987
8663959	86639591	8	~1987
8663969	121295567	9	~1987
8664451	86644511	8	~1987
8664671	17329343	8	~1985
8664869	121308167	9	~1987

Exp.	Prime Factor	Digits	Year
8665207	346608281	9	~1988
8665277	51991663	8	~1986
8665313	51991879	8	~1986
8665451	17330903	8	~1985
8665873	138653969	9	~1987
8665991	17331983	8	~1985
8666051	17332103	8	~1985
8666219	17332439	8	~1985
8666291	17332583	8	~1985
8666351	17332703	8	~1985
8666459	17332919	8	~1985
8667079	86670791	8	~1987
8667371	17334743	8	~1985
8667697	52006183	8	~1986
8668031	17336063	8	~1985
8668057	52008343	8	~1986
8668133	52008799	8	~1986
8668151	69345209	8	~1987
8668207	346728281	9	~1988
8668553	52011319	8	~1986
8668571	17337143	8	~1985
8668799	156038383	9	~1988
8668901	52013407	8	~1986
8669071	138705137	9	~1987
8669123	17338247	8	~1985

Exp.	Prime Factor	Digits	Year
8669159	17338319	8	~1985
8669233	52015399	8	~1986
8669293	52015759	8	~1986
8669351	69354809	8	~1987
8669483	17338967	8	~1985
8669543	17339087	8	~1985
8669627	69357017	8	~1987
8669879	17339759	8	~1985
8669993	52019959	8	~1986
8670071	17340143	8	~1985
8670281	52021687	8	~1986
8670373	208088953	9	~1988
8670491	156068839	9	~1988
8670679	208096297	9	~1988
8670713	52024279	8	~1986
8670743	17341487	8	~1985
8670989	121393847	9	~1987
8671057	52026343	8	~1986
8671499	69371993	8	~1987
8671511	17343023	8	~1985
8671721	52030327	8	~1986
8671919	17343839	8	~1985
8671937	69375497	8	~1987
8671979	17343959	8	~1985
8671979	69375833	8

5.307.017 digits

26-01-11