Small Mersenne Prime Factors (page 735/5025)

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
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
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

Exp.	Prime Factor	Digits	Year
5735711	11471423	8	~1984
5735747	45885977	8	~1985
5735771	11471543	8	~1984
5736431	11472863	8	~1984
5736481	34418887	8	~1985
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

Exp.	Prime Factor	Digits	Year
5739101	34434607	8	~1985
5739203	11478407	8	~1984
5739731	11479463	8	~1984
5739973	172199191	9	~1987
5740079	11480159	8	~1984
5740081	413285833	9	~1988
5740093	229603721	9	~1987
5740099	57400991	8	~1985
5740181	34441087	8	~1985
5740277	218130527	9	~1987
5740613	34443679	8	~1985
5740873	34445239	8	~1985
5740919	11481839	8	~1984
5740967	137783209	9	~1986
5741303	11482607	8	~1984
5741423	11482847	8	~1984
5741531	149279807	9	~1986
5741573	34449439	8	~1985
5741741	34450447	8	~1985
5741839	57418391	8	~1985
5741873	34451239	8	~1985
5742041	34452247	8	~1985
5742103	57421031	8	~1985
5742239	11484479	8	~1984
5742469	126334319	9	~1986

Exp.	Prime Factor	Digits	Year
5742509	183760289	9	~1987
5742563	11485127	8	~1984
5742619	57426191	8	~1985
5742713	723581839	9	~1988
5742851	11485703	8	~1984
5743051	91888817	8	~1986
5743201	34459207	8	~1985
5743357	34460143	8	~1985
5743481	45947849	8	~1985
5743667	103386007	9	~1986
5743691	11487383	8	~1984
5744003	11488007	8	~1984
5744267	45954137	8	~1985
5744311	91908977	8	~1986
5744353	34466119	8	~1985
5744477	34466863	8	~1985
5744663	11489327	8	~1984
5744803	91916849	8	~1986
5744803	241281727	9
5745023	11490047	8	~1984
5745197	34471183	8	~1985
5745203	11490407	8	~1984
5745263	11490527	8	~1984
5745599	11491199	8	~1984
5745671	11491343	8	~1984

4.724.182 digits

25-04-13