Small Mersenne Prime Factors (page 865/5025)

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
7561751	725928097	9	~1989
7561811	15123623	8	~1985
7562077	45372463	8	~1986
7562341	45374047	8	~1986
7562407	75624071	8	~1986
7562519	15125039	8	~1985
7562693	45376159	8	~1986
7562771	15125543	8	~1985
7563001	166386023	9	~1987
7563071	15126143	8	~1985
7563191	15126383	8	~1985
7563431	15126863	8	~1985
7563443	15126887	8	~1985
7563581	45381487	8	~1986
7563779	15127559	8	~1985
7563901	45383407	8	~1986
7564091	60512729	8	~1986
7564211	15128423	8	~1985
7564301	45385807	8	~1986
7564499	15128999	8	~1985
7564673	544656457	9	~1989
7564871	15129743	8	~1985
7564913	45389479	8	~1986
7565093	45390559	8	~1986
7565191	121043057	9	~1987

Exp.	Prime Factor	Digits	Year
7565303	15130607	8	~1985
7565423	15130847	8	~1985
7565483	15130967	8	~1985
7565531	15131063	8	~1985
7566059	15132119	8	~1985
7566061	45396367	8	~1986
7566131	15132263	8	~1985
7566281	45397687	8	~1986
7566659	60533273	8	~1986
7566803	15133607	8	~1985
7566899	15133799	8	~1985
7566983	15133967	8	~1985
7567099	136207783	9	~1987
7567891	620567063	9	~1989
7567919	15135839	8	~1985
7567991	15135983	8	~1985
7568303	15136607	8	~1985
7568399	15136799	8	~1985
7568531	15137063	8	~1985
7568699	15137399	8	~1985
7568741	45412447	8	~1986
7568777	45412663	8	~1986
7568879	60551033	8	~1986
7568999	15137999	8	~1985
7569119	15138239	8	~1985

Exp.	Prime Factor	Digits	Year
7569179	15138359	8	~1985
7569347	60554777	8	~1986
7569431	15138863	8	~1985
7569629	60557033	8	~1986
7569671	15139343	8	~1985
7569713	45418279	8	~1986
7569839	15139679	8	~1985
7569851	15139703	8	~1985
7569911	15139823	8	~1985
7570259	15140519	8	~1985
7570261	45421567	8	~1986
7570481	45422887	8	~1986
7570543	75705431	8	~1986
7570583	15141167	8	~1985
7570637	45423823	8	~1986
7570733	3876215297	10	~1991
7570991	15141983	8	~1985
7571351	15142703	8	~1985
7571423	15142847	8	~1985
7571437	45428623	8	~1986
7571537	60572297	8	~1986
7571539	75715391	8	~1986
7571563	75715631	8	~1986
7571777	45430663	8	~1986
7571821	45430927	8	~1986

Exp.	Prime Factor	Digits	Year
7572263	15144527	8	~1985
7572563	15145127	8	~1985
7572791	15145583	8	~1985
7572941	45437647	8	~1986
7573537	45441223	8	~1986
7573537	121176593	9
7573591	75735911	8	~1986
7573679	15147359	8	~1985
7573691	15147383	8	~1985
7573883	15147767	8	~1985
7573921	45443527	8	~1986
7574111	15148223	8	~1985
7574617	409029319	9	~1988
7574717	45448303	8	~1986
7574807	60598457	8	~1986
7574999	15149999	8	~1985
7575059	15150119	8	~1985
7575077	45450463	8	~1986
7575311	15150623	8	~1985
7575371	15150743	8	~1985
7575527	60604217	8	~1986
7575637	45453823	8	~1986
7575803	181819273	9	~1987
7575881	60607049	8	~1986
7575923	15151847	8	~1985

4.724.182 digits

25-04-13