Small Mersenne Prime Factors (page 743/5205)

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
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
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

Exp.	Prime Factor	Digits	Year
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
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

Exp.	Prime Factor	Digits	Year
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
5734439	11468879	8	~1984
5734493	34406959	8	~1985
5734691	11469383	8	~1984
5734873	34409239	8	~1985
5734973	34409839	8	~1985
5735003	11470007	8	~1984
5735033	34410199	8	~1985
5735047	367043009	9	~1987
5735063	11470127	8	~1984
5735179	516166111	9	~1988
5735287	137646889	9	~1986
5735357	34412143	8	~1985
5735617	34413703	8	~1985
5735711	11471423	8	~1984
5735747	45885977	8	~1985
5735771	11471543	8	~1984
5736431	11472863	8	~1984
5736481	34418887	8	~1985

Exp.	Prime Factor	Digits	Year
5736593	34419559	8	~1985
5736611	11473223	8	~1984
5736707	103260727	9	~1986
5736733	550726369	9	~1988
5736823	57368231	8	~1985
5736911	11473823	8	~1984
5737057	34422343	8	~1985
5737229	45897833	8	~1985
5737229	309810367	9
5737271	11474543	8	~1984
5737283	183593057	9	~1987
5737321	34423927	8	~1985
5737351	332766359	9	~1987
5737379	45899033	8	~1985
5737811	11475623	8	~1984
5738107	91809713	8	~1986
5738297	34429783	8	~1985
5738591	11477183	8	~1984
5738699	11477399	8	~1984
5738861	45910889	8	~1985
5739101	34434607	8	~1985
5739203	11478407	8	~1984
5739731	11479463	8	~1984
5739973	172199191	9	~1987
5740079	11480159	8	~1984

4.903.097 digits

25-07-08