Small Mersenne Prime Factors (page 732/5130)

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
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
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

Exp.	Prime Factor	Digits	Year
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
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

Exp.	Prime Factor	Digits	Year
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
5639411	45115289	8	~1985
5639497	33836983	8	~1985
5639617	90233873	8	~1986
5639723	11279447	8	~1984
5639867	45118937	8	~1985
5640119	11280239	8	~1984
5640389	135369337	9	~1986

Exp.	Prime Factor	Digits	Year
5640599	11281199	8	~1984
5640671	11281343	8	~1984
5640961	33845767	8	~1985
5640961	1308702953	10
5641159	56411591	8	~1985
5641379	11282759	8	~1984
5641577	45132617	8	~1985
5641711	56417111	8	~1985
5641837	33851023	8	~1985
5641931	11283863	8	~1984
5642083	56420831	8	~1985
5642099	11284199	8	~1984
5642233	33853399	8	~1985
5642381	45139049	8	~1985
5642477	169274311	9	~1987
5642531	11285063	8	~1984
5642633	33855799	8	~1985
5642783	11285567	8	~1984
5643059	270866833	9	~1987
5643227	45145817	8	~1985
5643301	33859807	8	~1985
5643479	11286959	8	~1984
5643553	33861319	8	~1985
5643563	11287127	8	~1984
5643607	56436071	8	~1985

4.828.532 digits

25-06-01