Small Mersenne Prime Factors (page 718/5490)

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
5250743	10501487	8	~1983
5250761	42006089	8	~1985
5250779	10501559	8	~1983
5250803	10501607	8	~1983
5250851	10501703	8	~1983
5251039	220543639	9	~1987
5251097	42008777	8	~1985
5251193	31507159	8	~1985
5251271	10502543	8	~1983
5251507	178551239	9	~1986
5251663	378119737	9	~1987
5251783	52517831	8	~1985
5251859	10503719	8	~1983
5251919	42015353	8	~1985
5252281	84036497	8	~1986
5252413	31514479	8	~1985
5252603	10505207	8	~1983
5252641	115558103	9	~1986
5252761	31516567	8	~1985
5253203	10506407	8	~1983
5253383	10506767	8	~1983
5253431	10506863	8	~1983
5253487	52534871	8	~1985
5253779	10507559	8	~1983
5253881	199647479	9	~1987

Exp.	Prime Factor	Digits	Year
5254019	42032153	8	~1985
5254163	10508327	8	~1983
5254247	42033977	8	~1985
5254637	73564919	8	~1986
5254721	31528327	8	~1985
5254831	52548311	8	~1985
5255069	168162209	9	~1986
5255101	31530607	8	~1985
5255113	31530679	8	~1985
5255233	31531399	8	~1985
5255479	52554791	8	~1985
5255527	126132649	9	~1986
5255531	10511063	8	~1983
5255617	126134809	9	~1986
5255773	84092369	8	~1986
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

Exp.	Prime Factor	Digits	Year
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
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

Exp.	Prime Factor	Digits	Year
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
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

5.187.277 digits

25-11-17