Small Mersenne Prime Factors (page 955/5460)

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
8534069	68272553	8	~1987
8534243	17068487	8	~1985
8534303	17068607	8	~1985
8534371	85343711	8	~1987
8534411	17068823	8	~1985
8534423	17068847	8	~1985
8534447	68275577	8	~1987
8534639	17069279	8	~1985
8534657	68277257	8	~1987
8534891	17069783	8	~1985
8535083	17070167	8	~1985
8535179	17070359	8	~1985
8535413	51212479	8	~1986
8535433	51212599	8	~1986
8535473	51212839	8	~1986
8535533	51213199	8	~1986
8535781	51214687	8	~1986
8535929	68287433	8	~1987
8536043	17072087	8	~1985
8536267	85362671	8	~1987
8536571	17073143	8	~1985
8536807	85368071	8	~1987
8536883	17073767	8	~1985
8537219	17074439	8	~1985
8537437	51224623	8	~1986

Exp.	Prime Factor	Digits	Year
8537467	85374671	8	~1987
8537603	17075207	8	~1985
8537747	68301977	8	~1987
8538143	17076287	8	~1985
8538371	17076743	8	~1985
8538599	631856327	9	~1989
8538611	17077223	8	~1985
8538833	51232999	8	~1986
8538851	17077703	8	~1985
8539051	85390511	8	~1987
8539057	51234343	8	~1986
8539067	204937609	9	~1988
8539259	17078519	8	~1985
8539259	68314073	8
8539691	17079383	8	~1985
8539889	68319113	8	~1987
8539913	119558783	9	~1987
8540237	119563319	9	~1987
8540537	51243223	8	~1986
8541359	17082719	8	~1985
8541397	51248383	8	~1986
8541409	187910999	9	~1988
8541479	17082959	8	~1985
8541479	68331833	8
8541503	17083007	8	~1985

Exp.	Prime Factor	Digits	Year
8541721	51250327	8	~1986
8541959	17083919	8	~1985
8541971	68335769	8	~1987
8542139	17084279	8	~1985
8542333	51253999	8	~1986
8542463	17084927	8	~1985
8542481	68339849	8	~1987
8542643	17085287	8	~1985
8542811	17085623	8	~1985
8542817	68342537	8	~1987
8543261	51259567	8	~1986
8543279	273384929	9	~1988
8543399	17086799	8	~1985
8543459	17086919	8	~1985
8543461	187956143	9	~1988
8543543	17087087	8	~1985
8543651	68349209	8	~1987
8543831	17087663	8	~1985
8543999	17087999	8	~1985
8544751	85447511	8	~1987
8544971	68359769	8	~1987
8545139	68361113	8	~1987
8545151	17090303	8	~1985
8545319	17090639	8	~1985
8545331	17090663	8	~1985

Exp.	Prime Factor	Digits	Year
8545571	17091143	8	~1985
8545939	205102537	9	~1988
8546423	17092847	8	~1985
8546437	136742993	9	~1987
8546467	641959322239	12	~1996
8546521	51279127	8	~1986
8546651	68373209	8	~1987
8546807	68374457	8	~1987
8547269	68378153	8	~1987
8547419	17094839	8	~1985
8547437	68379497	8	~1987
8547509	68380073	8	~1987
8547887	68383097	8	~1987
8547911	17095823	8	~1985
8547941	68383529	8	~1987
8548291	85482911	8	~1987
8548321	5522215367	10	~1991
8548453	51290719	8	~1986
8548559	68388473	8	~1987
8548781	51292687	8	~1986
8548817	51292903	8	~1986
8548831	136781297	9	~1987
8549201	51295207	8	~1986
8549201	68393609	8
8549797	136796753	9	~1987

5.157.210 digits

25-11-02