Small Mersenne Prime Factors (page 337/5190)

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
1624151	3248303	7	~1979
1624159	16241591	8	~1981
1624213	64968521	8	~1983
1624241	9745447	7	~1981
1624331	12994649	8	~1981
1624607	42239783	8	~1982
1624661	12997289	8	~1981
1624691	42241967	8	~1982
1624691	146222191	9
1624913	9749479	7	~1981
1625171	3250343	7	~1979
1625201	48756031	8	~1982
1625287	39006889	8	~1982
1625321	48759631	8	~1982
1625339	3250679	7	~1979
1625417	22755839	8	~1982
1625419	55264247	8	~1982
1625497	26007953	8	~1982
1625699	3251399	7	~1979
1625707	55274039	8	~1982
1625749	143065913	9	~1984
1625759	3251519	7	~1979
1625831	3251663	7	~1979
1625867	39020809	8	~1982
1625909	13007273	8	~1981

Exp.	Prime Factor	Digits	Year
1625927	13007417	8	~1981
1626017	22764239	8	~1982
1626127	39027049	8	~1982
1626173	9757039	7	~1981
1626211	68300863	8	~1983
1626227	13009817	8	~1981
1626239	393549839	9	~1985
1626263	3252527	7	~1979
1626281	9757687	7	~1981
1626377	9758263	7	~1981
1626431	3252863	7	~1979
1626431	42287207	8
1626431	52045793	8
1626433	9758599	7	~1981
1626481	9758887	7	~1981
1626589	165912079	9	~1984
1626613	87837103	8	~1983
1626617	61811447	8	~1983
1626739	182194769	9	~1984
1626881	13015049	8	~1981
1626893	9761359	7	~1981
1626979	16269791	8	~1981
1626983	3253967	7	~1979
1627013	9762079	7	~1981
1627063	26033009	8	~1982

Exp.	Prime Factor	Digits	Year
1627079	3254159	7	~1979
1627117	9762703	7	~1981
1627337	61838807	8	~1983
1627357	39056569	8	~1982
1627403	3254807	7	~1979
1627403	130192241	9
1627489	152983967	9	~1984
1627607	42317783	8	~1982
1627793	9766759	7	~1981
1627883	3255767	7	~1979
1628131	16281311	8	~1981
1628171	52101473	8	~1982
1628309	22796327	8	~1982
1628359	39080617	8	~1982
1628369	22797167	8	~1982
1628489	78167473	8	~1983
1628701	35831423	8	~1982
1628773	9772639	7	~1981
1628801	130304081	9	~1983
1629071	42355847	8	~1982
1629077	9774463	7	~1981
1629109	39098617	8	~1982
1629119	13032953	8	~1981
1629137	39099289	8	~1982
1629163	16291631	8	~1981

Exp.	Prime Factor	Digits	Year
1629233	9775399	7	~1981
1629253	65170121	8	~1983
1629319	29327743	8	~1982
1629359	3258719	7	~1979
1629361	9776167	7	~1981
1629431	3258863	7	~1979
1629541	205322167	9	~1984
1629547	5475277921	10	~1987
1629559	772410967	9	~1985
1629599	3259199	7	~1979
1629599	29332783	8
1629731	3259463	7	~1979
1629731	42373007	8
1629851	3259703	7	~1979
1629899	3259799	7	~1979
1629997	9779983	7	~1981
1630049	805244207	9	~1985
1630051	16300511	8	~1981
1630141	35863103	8	~1982
1630169	48905071	8	~1982
1630303	39127273	8	~1982
1630451	3260903	7	~1979
1630457	9782743	7	~1981
1630619	68485999	8	~1983
1630813	48924391	8	~1982

4.888.230 digits

25-06-29