Small Mersenne Prime Factors (page 717/5460)

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
5255819	10511639	8	~1983
5255863	52558631	8	~1985
5256137	31536823	8	~1985
5256239	10512479	8	~1983
5256253	157687591	9	~1986
5256341	31538047	8	~1985
5256371	10512743	8	~1983
5256661	31539967	8	~1985
5256683	10513367	8	~1983
5256751	52567511	8	~1985
5256851	10513703	8	~1983
5257079	10514159	8	~1983
5257157	31542943	8	~1985
5257361	31544167	8	~1985
5257463	10514927	8	~1983
5257793	31546759	8	~1985
5258063	10516127	8	~1983
5258171	10516343	8	~1983
5258171	42065369	8
5258303	10516607	8	~1983
5258399	10516799	8	~1983
5258489	42067913	8	~1985
5258531	10517063	8	~1983
5258639	94655503	8	~1986
5258683	178795223	9	~1986

Exp.	Prime Factor	Digits	Year
5258723	10517447	8	~1983
5259011	10518023	8	~1983
5259071	10518143	8	~1983
5259151	84146417	8	~1986
5259263	10518527	8	~1983
5259311	10518623	8	~1983
5259413	31556479	8	~1985
5259563	10519127	8	~1983
5259671	10519343	8	~1983
5259689	126232537	9	~1986
5259731	10519463	8	~1983
5260051	52600511	8	~1985
5260117	31560703	8	~1985
5260139	42081113	8	~1985
5260337	31562023	8	~1985
5260379	42083033	8	~1985
5260439	10520879	8	~1983
5260487	42083897	8	~1985
5260679	10521359	8	~1983
5260799	42086393	8	~1985
5260883	10521767	8	~1983
5260943	10521887	8	~1983
5261051	10522103	8	~1983
5261153	31566919	8	~1985
5261261	199927919	9	~1987

Exp.	Prime Factor	Digits	Year
5261471	10522943	8	~1983
5261647	94709647	8	~1986
5261741	31570447	8	~1985
5261783	10523567	8	~1983
5261941	84191057	8	~1986
5262001	31572007	8	~1985
5262329	168394529	9	~1986
5262371	10524743	8	~1983
5262539	10525079	8	~1983
5262557	73675799	8	~1986
5262599	10525199	8	~1983
5262611	42100889	8	~1985
5262863	10525727	8	~1983
5263033	84208529	8	~1986
5263241	31579447	8	~1985
5263499	168431969	9	~1986
5263541	31581247	8	~1985
5263561	31581367	8	~1985
5263631	42109049	8	~1985
5263637	42109097	8	~1985
5263733	31582399	8	~1985
5264381	31586287	8	~1985
5264443	84231089	8	~1986
5264477	73702679	8	~1986
5264537	31587223	8	~1985

Exp.	Prime Factor	Digits	Year
5264683	52646831	8	~1985
5264801	42118409	8	~1985
5265059	10530119	8	~1983
5265067	52650671	8	~1985
5265131	10530263	8	~1983
5265193	31591159	8	~1985
5265193	115834247	9
5265473	73716623	8	~1986
5266031	10532063	8	~1983
5266271	42130169	8	~1985
5266441	31598647	8	~1985
5266673	31600039	8	~1985
5266799	10533599	8	~1983
5266883	10533767	8	~1983
5266907	42135257	8	~1985
5266979	10533959	8	~1983
5266997	126407929	9	~1986
5267159	221220679	9	~1987
5267257	158017711	9	~1986
5267323	84277169	8	~1986
5267519	10535039	8	~1983
5267711	10535423	8	~1983
5267783	547849433	9	~1988
5268031	52680311	8	~1985
5268083	10536167	8	~1983

5.157.210 digits

25-11-02