Small Mersenne Prime Factors (page 1004/6225)

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
8642237	69137897	8	~1987
8642861	51857167	8	~1986
8643083	17286167	8	~1985
8643143	17286287	8	~1985
8643337	605033591	9	~1989
8643443	17286887	8	~1985
8643521	69148169	8	~1987
8643671	17287343	8	~1985
8643697	51862183	8	~1986
8643797	69150377	8	~1987
8643839	17287679	8	~1985
8643851	17287703	8	~1985
8643893	121014503	9	~1987
8643941	259318231	9	~1988
8643941	829818337	9
8644019	17288039	8	~1985
8644049	69152393	8	~1987
8644057	138304913	9	~1987
8644679	17289359	8	~1985
8644949	69159593	8	~1987
8644957	345798281	9	~1988
8644991	17289983	8	~1985
8645243	17290487	8	~1985
8645341	51872047	8	~1986
8645597	51873583	8	~1986

Exp.	Prime Factor	Digits	Year
8645633	207495193	9	~1988
8645761	138332177	9	~1987
8645773	190207007	9	~1988
8646293	51877759	8	~1986
8646299	17292599	8	~1985
8646317	69170537	8	~1987
8646401	69171209	8	~1987
8646503	17293007	8	~1985
8646779	17293559	8	~1985
8646899	17293799	8	~1985
8646947	69175577	8	~1987
8646971	17293943	8	~1985
8647061	69176489	8	~1987
8647181	51883087	8	~1986
8647657	51885943	8	~1986
8647697	69181577	8	~1987
8647759	155659663	9	~1988
8647817	51886903	8	~1986
8647979	17295959	8	~1985
8648113	51888679	8	~1986
8648369	536198879	9	~1989
8648447	69187577	8	~1987
8648459	17296919	8	~1985
8648677	51892063	8	~1986
8648729	69189833	8	~1987

Exp.	Prime Factor	Digits	Year
8649191	17298383	8	~1985
8649191	69193529	8
8649197	69193577	8	~1987
8649241	51895447	8	~1986
8649293	51895759	8	~1986
8649409	4134417503	10	~1991
8649451	86494511	8	~1987
8649451	138391217	9
8649479	17298959	8	~1985
8649581	51897487	8	~1986
8649611	17299223	8	~1985
8649671	17299343	8	~1985
8649671	69197369	8
8650151	17300303	8	~1985
8650211	69201689	8	~1987
8650423	294114383	9	~1988
8650667	69205337	8	~1987
8650793	51904759	8	~1986
8650919	17301839	8	~1985
8651051	69208409	8	~1987
8651063	17302127	8	~1985
8651231	69209849	8	~1987
8651399	17302799	8	~1985
8651579	17303159	8	~1985
8651603	17303207	8	~1985

Exp.	Prime Factor	Digits	Year
8651609	121122527	9	~1987
8651953	51911719	8	~1986
8651999	17303999	8	~1985
8652023	17304047	8	~1985
8652257	69218057	8	~1987
8652359	17304719	8	~1985
8652359	69218873	8
8652401	51914407	8	~1986
8652641	69221129	8	~1987
8652731	69221849	8	~1987
8652781	51916687	8	~1986
8652821	51916927	8	~1986
8652863	17305727	8	~1985
8653261	190371743	9	~1988
8653343	17306687	8	~1985
8653679	17307359	8	~1985
8653691	17307383	8	~1985
8653691	69229529	8
8654183	17308367	8	~1985
8654201	51925207	8	~1986
8654231	17308463	8	~1985
8654333	51925999	8	~1986
8654917	138478673	9	~1987
8655011	17310023	8	~1985
8655071	17310143	8	~1985

5.920.543 digits

26-10-25