Small Mersenne Prime Factors (page 935/5205)

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
8466961	135471377	9	~1987
8467111	152407999	9	~1987
8467271	16934543	8	~1985
8467409	457240087	9	~1989
8467499	16934999	8	~1985
8467523	16935047	8	~1985
8467637	50805823	8	~1986
8467637	67741097	8
8468077	50808463	8	~1986
8468123	16936247	8	~1985
8468293	338731721	9	~1988
8468441	50810647	8	~1986
8468561	50811367	8	~1986
8468897	50813383	8	~1986
8468903	16937807	8	~1985
8468963	16937927	8	~1985
8469239	16938479	8	~1985
8469271	135508337	9	~1987
8469431	67755449	8	~1987
8469491	16938983	8	~1985
8470109	67760873	8	~1987
8470381	50822287	8	~1986
8470421	67763369	8	~1987
8470589	67764713	8	~1987
8470597	254117911	9	~1988

Exp.	Prime Factor	Digits	Year
8470681	50824087	8	~1986
8471069	67768553	8	~1987
8471531	16943063	8	~1985
8471581	50829487	8	~1986
8471849	118605887	9	~1987
8471917	50831503	8	~1986
8472053	50832319	8	~1986
8472127	203331049	9	~1988
8472203	16944407	8	~1985
8472259	406668433	9	~1988
8472337	50834023	8	~1986
8472433	50834599	8	~1986
8472479	16944959	8	~1985
8472539	16945079	8	~1985
8472617	50835703	8	~1986
8472847	84728471	8	~1987
8472923	16945847	8	~1985
8473097	50838583	8	~1986
8473141	186409103	9	~1988
8473631	16947263	8	~1985
8473739	16947479	8	~1985
8473901	67791209	8	~1987
8474159	16948319	8	~1985
8474183	16948367	8	~1985
8474353	50846119	8	~1986

Exp.	Prime Factor	Digits	Year
8474357	50846143	8	~1986
8474363	16948727	8	~1985
8474663	16949327	8	~1985
8474723	16949447	8	~1985
8474777	50848663	8	~1986
8474911	84749111	8	~1987
8475067	84750671	8	~1987
8475191	16950383	8	~1985
8475323	220358399	9	~1988
8475563	16951127	8	~1985
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

Exp.	Prime Factor	Digits	Year
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
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
8479703	16959407	8	~1985
8479799	16959599	8	~1985
8479979	16959959	8	~1985
8480063	16960127	8	~1985
8480177	474889913	9	~1989
8480243	16960487	8	~1985

4.903.097 digits

25-07-08