Small Mersenne Prime Factors (page 758/5550)

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
5721971	102995479	9	~1986
5722153	34332919	8	~1985
5722201	34333207	8	~1985
5722271	45778169	8	~1985
5722279	57222791	8	~1985
5722313	34333879	8	~1985
5722333	137335993	9	~1986
5722499	11444999	8	~1984
5722513	34335079	8	~1985
5722621	34335727	8	~1985
5722637	34335823	8	~1985
5722991	11445983	8	~1984
5723147	45785177	8	~1985
5723593	263285279	9	~1987
5723639	11447279	8	~1984
5723719	137369257	9	~1986
5724013	171720391	9	~1987
5724137	34344823	8	~1985
5724143	11448287	8	~1984
5724157	34344943	8	~1985
5724197	45793577	8	~1985
5724581	45796649	8	~1985
5724683	11449367	8	~1984
5724787	57247871	8	~1985
5724811	57248111	8	~1985

Exp.	Prime Factor	Digits	Year
5725001	45800009	8	~1985
5725081	34350487	8	~1985
5725241	45801929	8	~1985
5725259	11450519	8	~1984
5725283	11450567	8	~1984
5725331	45802649	8	~1985
5725457	45803657	8	~1985
5725457	80156399	8
5725547	45804377	8	~1985
5725679	45805433	8	~1985
5725739	45805913	8	~1985
5725883	11451767	8	~1984
5725927	57259271	8	~1985
5725943	11451887	8	~1984
5725981	34355887	8	~1985
5726023	194684783	9	~1987
5726111	11452223	8	~1984
5726153	80166143	8	~1986
5726191	103071439	9	~1986
5726711	11453423	8	~1984
5726761	34360567	8	~1985
5726827	57268271	8	~1985
5726843	1202637031	10	~1989
5727017	45816137	8	~1985
5727221	45817769	8	~1985

Exp.	Prime Factor	Digits	Year
5727427	57274271	8	~1985
5727697	34366183	8	~1985
5727719	11455439	8	~1984
5727919	57279191	8	~1985
5728199	11456399	8	~1984
5728279	57282791	8	~1985
5728301	34369807	8	~1985
5728579	57285791	8	~1985
5728733	34372399	8	~1985
5728781	34372687	8	~1985
5729039	11458079	8	~1984
5729099	11458199	8	~1984
5729359	653146927	9	~1988
5729453	80212343	8	~1986
5729579	45836633	8	~1985
5729597	34377583	8	~1985
5729827	57298271	8	~1985
5729839	57298391	8	~1985
5730007	57300071	8	~1985
5730251	11460503	8	~1984
5730311	11460623	8	~1984
5730407	103147327	9	~1986
5730539	137532937	9	~1986
5730743	11461487	8	~1984
5730773	34384639	8	~1985

Exp.	Prime Factor	Digits	Year
5730899	11461799	8	~1984
5731619	11463239	8	~1984
5731679	11463359	8	~1984
5731811	45854489	8	~1985
5731949	80247287	8	~1986
5732131	57321311	8	~1985
5732341	1272579703	10	~1989
5732591	11465183	8	~1984
5732599	57325991	8	~1985
5732711	11465423	8	~1984
5732711	45861689	8
5732809	275174833	9	~1987
5732999	11465999	8	~1984
5733241	126131303	9	~1986
5733551	11467103	8	~1984
5733613	91737809	8	~1986
5733661	34401967	8	~1985
5733691	57336911	8	~1985
5733719	45869753	8	~1985
5733919	366970817	9	~1987
5733997	34403983	8	~1985
5734021	34404127	8	~1985
5734103	11468207	8	~1984
5734343	11468687	8	~1984
5734357	34406143	8	~1985

5.247.179 digits

25-12-14