Small Mersenne Prime Factors (page 875/5025)

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
7712213	107970983	9	~1987
7712219	15424439	8	~1985
7712729	61701833	8	~1986
7712819	15425639	8	~1985
7713071	15426143	8	~1985
7713071	61704569	8
7713077	107983079	9	~1987
7713127	308525081	9	~1988
7713569	61708553	8	~1986
7713613	46281679	8	~1986
7713659	246837089	9	~1988
7713701	46282207	8	~1986
7714111	77141111	8	~1986
7714571	15429143	8	~1985
7714621	46287727	8	~1986
7714757	61718057	8	~1986
7714921	231447631	9	~1988
7715053	46290319	8	~1986
7715423	15430847	8	~1985
7715549	108017687	9	~1987
7715579	15431159	8	~1985
7715723	15431447	8	~1985
7715891	15431783	8	~1985
7716019	77160191	8	~1986
7716281	46297687	8	~1986

Exp.	Prime Factor	Digits	Year
7716503	15433007	8	~1985
7716517	46299103	8	~1986
7716713	46300279	8	~1986
7716743	15433487	8	~1985
7716767	61734137	8	~1986
7716899	15433799	8	~1985
7717001	46302007	8	~1986
7717043	15434087	8	~1985
7717331	15434663	8	~1985
7717499	15434999	8	~1985
7717751	15435503	8	~1985
7717883	15435767	8	~1985
7718159	15436319	8	~1985
7718177	46309063	8	~1986
7718327	61746617	8	~1986
7718393	46310359	8	~1986
7718407	77184071	8	~1986
7718413	185241913	9	~1987
7718471	15436943	8	~1985
7718939	15437879	8	~1985
7718993	46313959	8	~1986
7719197	46315183	8	~1986
7719311	15438623	8	~1985
7719359	15438719	8	~1985
7719763	633020567	9	~1989

Exp.	Prime Factor	Digits	Year
7719841	46319047	8	~1986
7719923	15439847	8	~1985
7720241	370571569	9	~1988
7720451	15440903	8	~1985
7720561	46323367	8	~1986
7720871	15441743	8	~1985
7721251	77212511	8	~1986
7721293	355179479	9	~1988
7721303	15442607	8	~1985
7721369	61770953	8	~1986
7721501	46329007	8	~1986
7721891	15443783	8	~1985
7721977	46331863	8	~1986
7722017	108108239	9	~1987
7722119	15444239	8	~1985
7722443	15444887	8	~1985
7722623	15445247	8	~1985
7722791	15445583	8	~1985
7722833	417032983	9	~1988
7722931	77229311	8	~1986
7723097	61784777	8	~1986
7723283	15446567	8	~1985
7723511	15447023	8	~1985
7723679	15447359	8	~1985
7723721	46342327	8	~1986

Exp.	Prime Factor	Digits	Year
7723817	61790537	8	~1986
7723973	46343839	8	~1986
7723979	15447959	8	~1985
7724371	77243711	8	~1986
7724741	61797929	8	~1986
7724753	108146543	9	~1987
7724771	15449543	8	~1985
7724891	15449783	8	~1985
7725299	15450599	8	~1985
7725433	46352599	8	~1986
7725611	15451223	8	~1985
7725709	2580386807	10	~1990
7725911	15451823	8	~1985
7725959	61807673	8	~1986
7726139	15452279	8	~1985
7726261	46357567	8	~1986
7726343	15452687	8	~1985
7726391	15452783	8	~1985
7726469	61811753	8	~1986
7726679	15453359	8	~1985
7727099	15454199	8	~1985
7727233	46363399	8	~1986
7727359	77273591	8	~1986
7728179	15456359	8	~1985
7728293	46369759	8	~1986

4.724.182 digits

25-04-13