Small Mersenne Prime Factors (page 718/5775)

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
5117083	51170831	8	~1985
5117117	40936937	8	~1985
5117363	10234727	8	~1983
5117471	10234943	8	~1983
5117551	51175511	8	~1985
5117687	40941497	8	~1985
5118013	30708079	8	~1985
5118089	40944713	8	~1985
5118143	10236287	8	~1983
5118203	10236407	8	~1983
5118341	30710047	8	~1985
5118359	10236719	8	~1983
5118637	30711823	8	~1985
5119043	10238087	8	~1983
5119139	10238279	8	~1983
5119199	10238399	8	~1983
5119319	10238639	8	~1983
5119319	40954553	8
5119463	10238927	8	~1983
5119571	10239143	8	~1983
5119637	30717823	8	~1985
5119841	194553959	9	~1987
5119871	40958969	8	~1985
5119909	112637999	9	~1986
5119973	30719839	8	~1985

Exp.	Prime Factor	Digits	Year
5120263	51202631	8	~1985
5120371	81925937	8	~1986
5120597	276512239	9	~1987
5120657	30723943	8	~1985
5120831	10241663	8	~1983
5120957	40967657	8	~1985
5120957	71693399	8
5120963	10241927	8	~1983
5121209	40969673	8	~1985
5121323	10242647	8	~1983
5121353	30728119	8	~1985
5121359	10242719	8	~1983
5121667	81946673	8	~1986
5121821	30730927	8	~1985
5121841	30731047	8	~1985
5121911	10243823	8	~1983
5122121	30732727	8	~1985
5122277	71711879	8	~1985
5122433	71714063	8	~1985
5122679	10245359	8	~1983
5122739	10245479	8	~1983
5122889	71720447	8	~1985
5122919	10245839	8	~1983
5122961	40983689	8	~1985
5123003	10246007	8	~1983

Exp.	Prime Factor	Digits	Year
5123197	30739183	8	~1985
5123231	10246463	8	~1983
5123281	81972497	8	~1986
5123771	10247543	8	~1983
5124011	10248023	8	~1983
5124131	368937433	9	~1987
5124253	122982073	9	~1986
5124443	133235519	9	~1986
5124491	502200119	9	~1988
5124683	10249367	8	~1983
5125073	317754527	9	~1987
5125201	645775327	9	~1988
5125273	30751639	8	~1985
5125321	2337146377	10	~1989
5125511	10251023	8	~1983
5125733	5853587087	10	~1990
5125811	41006489	8	~1985
5125931	10251863	8	~1983
5126003	10252007	8	~1983
5126123	10252247	8	~1983
5126483	10252967	8	~1983
5126603	10253207	8	~1983
5126753	30760519	8	~1985
5126819	41014553	8	~1985
5126909	123045817	9	~1986

Exp.	Prime Factor	Digits	Year
5126959	51269591	8	~1985
5126963	10253927	8	~1983
5126971	51269711	8	~1985
5126977	358888391	9	~1987
5127203	10254407	8	~1983
5127341	30764047	8	~1985
5127481	82039697	8	~1986
5127839	41022713	8	~1985
5127971	10255943	8	~1983
5128297	153848911	9	~1986
5128337	30770023	8	~1985
5128337	41026697	8
5128351	92310319	8	~1986
5128391	10256783	8	~1983
5128523	10257047	8	~1983
5128583	10257167	8	~1983
5128691	10257383	8	~1983
5128817	71803439	8	~1985
5128859	10257719	8	~1983
5128867	92319607	8	~1986
5128973	71805623	8	~1985
5129129	41033033	8	~1985
5129171	10258343	8	~1983
5129177	153875311	9	~1986
5129197	30775183	8	~1985

5.471.290 digits

26-03-29