Small Mersenne Prime Factors (page 734/5190)

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
5621437	33728623	8	~1985
5621471	44971769	8	~1985
5621687	44973497	8	~1985
5621753	33730519	8	~1985
5621857	33731143	8	~1985
5621873	33731239	8	~1985
5621899	56218991	8	~1985
5621939	11243879	8	~1984
5622059	44976473	8	~1985
5622251	11244503	8	~1984
5622319	56223191	8	~1985
5622473	33734839	8	~1985
5622479	44979833	8	~1985
5622497	33734983	8	~1985
5622899	11245799	8	~1984
5623099	56230991	8	~1985
5623193	33739159	8	~1985
5623193	179942177	9
5623199	11246399	8	~1984
5623283	11246567	8	~1984
5623283	449862641	9
5623301	33739807	8	~1985
5623619	11247239	8	~1984
5623619	101225143	9
5624039	11248079	8	~1984

Exp.	Prime Factor	Digits	Year
5624243	11248487	8	~1984
5624327	101237887	9	~1986
5624471	11248943	8	~1984
5624527	89992433	8	~1986
5624651	44997209	8	~1985
5625071	101251279	9	~1986
5625421	663799679	9	~1988
5625461	45003689	8	~1985
5626051	56260511	8	~1985
5626079	11252159	8	~1984
5626259	11252519	8	~1984
5626619	11253239	8	~1984
5626703	146294279	9	~1986
5626837	33761023	8	~1985
5626969	360126017	9	~1987
5627009	135048217	9	~1986
5627053	33762319	8	~1985
5627177	33763063	8	~1985
5627197	33763183	8	~1985
5627519	11255039	8	~1984
5627641	33765847	8	~1985
5627717	45021737	8	~1985
5627849	45022793	8	~1985
5628131	270150289	9	~1987
5628367	56283671	8	~1985

Exp.	Prime Factor	Digits	Year
5628397	33770383	8	~1985
5628443	11256887	8	~1984
5628509	45028073	8	~1985
5628719	11257439	8	~1984
5628839	11257679	8	~1984
5628863	180123617	9	~1987
5629157	33774943	8	~1985
5629223	135101353	9	~1986
5629387	56293871	8	~1985
5629649	45037193	8	~1985
5629763	11259527	8	~1984
5630279	45042233	8	~1985
5630351	11260703	8	~1984
5630369	45042953	8	~1985
5630477	33782863	8	~1985
5630759	11261519	8	~1984
5631221	45049769	8	~1985
5631287	45050297	8	~1985
5631299	11262599	8	~1984
5631317	78838439	8	~1986
5631361	90101777	8	~1986
5631421	33788527	8	~1985
5631623	11263247	8	~1984
5631761	45054089	8	~1985
5631973	33791839	8	~1985

Exp.	Prime Factor	Digits	Year
5632001	33792007	8	~1985
5632043	11264087	8	~1984
5632093	33792559	8	~1985
5632387	56323871	8	~1985
5632391	11264783	8	~1984
5632439	11264879	8	~1984
5632541	33795247	8	~1985
5632637	33795823	8	~1985
5632651	56326511	8	~1985
5632751	11265503	8	~1984
5632799	11265599	8	~1984
5632807	901249121	9	~1988
5632853	33797119	8	~1985
5632859	45062873	8	~1985
5632883	11265767	8	~1984
5632993	90127889	8	~1986
5633363	11266727	8	~1984
5633521	33801127	8	~1985
5633651	11267303	8	~1984
5633759	11267519	8	~1984
5633807	45070457	8	~1985
5633833	33802999	8	~1985
5634061	33804367	8	~1985
5634061	405652393	9
5634427	56344271	8	~1985

4.888.230 digits

25-06-29