Small Mersenne Prime Factors (page 735/5205)

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
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
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

Exp.	Prime Factor	Digits	Year
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
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

Exp.	Prime Factor	Digits	Year
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
5634617	33807703	8	~1985
5634817	270471217	9	~1987
5635141	169054231	9	~1987
5635243	56352431	8	~1985
5635291	56352911	8	~1985
5635297	33811783	8	~1985
5635417	33812503	8	~1985
5635499	11270999	8	~1984
5635499	45083993	8
5635589	78898247	8	~1986

Exp.	Prime Factor	Digits	Year
5635807	225432281	9	~1987
5635921	33815527	8	~1985
5635921	90174737	8
5635961	33815767	8	~1985
5636131	90178097	8	~1986
5636153	33816919	8	~1985
5636161	33816967	8	~1985
5636249	180359969	9	~1987
5636251	90180017	8	~1986
5636383	56363831	8	~1985
5636399	11272799	8	~1984
5636747	45093977	8	~1985
5637059	11274119	8	~1984
5637143	11274287	8	~1984
5637563	11275127	8	~1984
5637637	360808769	9	~1987
5637743	11275487	8	~1984
5637811	90204977	8	~1986
5637953	78931343	8	~1986
5638103	11276207	8	~1984
5638397	270643057	9	~1987
5638601	33831607	8	~1985
5638631	146604407	9	~1986
5638751	11277503	8	~1984
5638799	11277599	8	~1984

4.903.097 digits

25-07-08