Small Mersenne Prime Factors (page 951/5460)

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
8475671	16951343	8	~1985
8475689	203416537	9	~1988
8475793	50854759	8	~1986
8475899	16951799	8	~1985
8476001	67808009	8	~1987
8476159	152570863	9	~1987
8476379	67811033	8	~1987
8476571	16953143	8	~1985
8476691	16953383	8	~1985
8476757	50860543	8	~1986
8476763	16953527	8	~1985
8476823	16953647	8	~1985
8476883	16953767	8	~1985
8476991	16953983	8	~1985
8477099	16954199	8	~1985
8477219	16954439	8	~1985
8477431	84774311	8	~1987
8477453	50864719	8	~1986
8477783	16955567	8	~1985
8477881	50867287	8	~1986
8478013	135648209	9	~1987
8478083	16956167	8	~1985
8478131	16956263	8	~1985
8478269	932609591	9	~1989
8478383	203481193	9	~1988

Exp.	Prime Factor	Digits	Year
8478521	50871127	8	~1986
8478551	16957103	8	~1985
8478623	16957247	8	~1985
8478629	67829033	8	~1987
8478719	16957439	8	~1985
8478803	16957607	8	~1985
8478893	50873359	8	~1986
8479043	16958087	8	~1985
8479511	16959023	8	~1985
8479649	67837193	8	~1987
8479703	16959407	8	~1985
8479799	16959599	8	~1985
8479979	16959959	8	~1985
8480063	16960127	8	~1985
8480177	474889913	9	~1989
8480243	16960487	8	~1985
8480249	67841993	8	~1987
8480249	254407471	9
8480617	542759489	9	~1989
8480621	50883727	8	~1986
8480651	16961303	8	~1985
8480699	67845593	8	~1987
8481059	16962119	8	~1985
8481437	50888623	8	~1986
8481461	50888767	8	~1986

Exp.	Prime Factor	Digits	Year
8481461	67851689	8
8481481	135703697	9	~1987
8481881	50891287	8	~1986
8481911	16963823	8	~1985
8481983	16963967	8	~1985
8482277	50893663	8	~1986
8482343	16964687	8	~1985
8482403	16964807	8	~1985
8482559	67860473	8	~1987
8482913	50897479	8	~1986
8483003	16966007	8	~1985
8483261	50899567	8	~1986
8483539	84835391	8	~1987
8483593	50901559	8	~1986
8483653	50901919	8	~1986
8483759	16967519	8	~1985
8483779	84837791	8	~1987
8483897	50903383	8	~1986
8483963	16967927	8	~1985
8484053	50904319	8	~1986
8484149	67873193	8	~1987
8484181	50905087	8	~1986
8484577	50907463	8	~1986
8485199	16970399	8	~1985
8485327	84853271	8	~1987

Exp.	Prime Factor	Digits	Year
8485331	16970663	8	~1985
8485391	16970783	8	~1985
8485517	203652409	9	~1988
8485619	16971239	8	~1985
8485859	16971719	8	~1985
8485891	356407423	9	~1988
8486117	50916703	8	~1986
8486197	50917183	8	~1986
8486279	16972559	8	~1985
8486339	16972679	8	~1985
8486399	356428759	9	~1988
8486717	254601511	9	~1988
8487173	50923039	8	~1986
8487239	16974479	8	~1985
8487293	50923759	8	~1986
8487293	203695033	9
8487863	16975727	8	~1985
8487953	50927719	8	~1986
8488379	16976759	8	~1985
8488583	16977167	8	~1985
8488871	16977743	8	~1985
8488919	16977839	8	~1985
8489011	84890111	8	~1987
8489053	50934319	8	~1986
8489357	50936143	8	~1986

5.157.210 digits

25-11-02