Small Mersenne Prime Factors (page 947/5490)

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
8393969	67151753	8	~1987
8394017	50364103	8	~1986
8394037	201456889	9	~1988
8394041	50364247	8	~1986
8394083	805831969	9	~1989
8394377	67155017	8	~1987
8394469	251834071	9	~1988
8394539	16789079	8	~1985
8394613	50367679	8	~1986
8394689	67157513	8	~1987
8394803	16789607	8	~1985
8394983	16789967	8	~1985
8395043	16790087	8	~1985
8395061	50370367	8	~1986
8395067	67160537	8	~1987
8395097	50370583	8	~1986
8395133	50370799	8	~1986
8395151	16790303	8	~1985
8395319	16790639	8	~1985
8395351	83953511	8	~1987
8395741	50374447	8	~1986
8395811	16791623	8	~1985
8395951	83959511	8	~1987
8395997	67167977	8	~1987
8396039	16792079	8	~1985

Exp.	Prime Factor	Digits	Year
8396281	50377687	8	~1986
8396413	50378479	8	~1986
8396519	67172153	8	~1987
8396761	50380567	8	~1986
8396779	151142023	9	~1987
8396819	67174553	8	~1987
8396953	50381719	8	~1986
8396987	67175897	8	~1987
8397079	83970791	8	~1987
8397217	50383303	8	~1986
8397353	50384119	8	~1986
8398393	50390359	8	~1986
8398619	16797239	8	~1985
8398633	50391799	8	~1986
8398757	50392543	8	~1986
8398913	50393479	8	~1986
8399057	50394343	8	~1986
8399057	67192457	8
8399107	83991071	8	~1987
8399401	50396407	8	~1986
8399621	50397727	8	~1986
8399701	403185649	9	~1988
8399773	50398639	8	~1986
8400011	16800023	8	~1985
8400061	50400367	8	~1986

Exp.	Prime Factor	Digits	Year
8400317	67202537	8	~1987
8400593	50403559	8	~1986
8400731	67205849	8	~1987
8401117	50406703	8	~1986
8401637	50409823	8	~1986
8401681	184836983	9	~1988
8401741	50410447	8	~1986
8401807	134428913	9	~1987
8401901	67215209	8	~1987
8402111	16804223	8	~1985
8402183	16804367	8	~1985
8402497	50414983	8	~1986
8402629	184857839	9	~1988
8402803	84028031	8	~1987
8402951	16805903	8	~1985
8402969	67223753	8	~1987
8403067	151255207	9	~1987
8403179	16806359	8	~1985
8403217	201677209	9	~1988
8403337	50420023	8	~1986
8403599	16807199	8	~1985
8403959	16807919	8	~1985
8404283	16808567	8	~1985
8404553	50427319	8	~1986
8404703	16809407	8	~1985

Exp.	Prime Factor	Digits	Year
8404819	151286743	9	~1987
8404819	285763847	9
8405003	16810007	8	~1985
8405219	16810439	8	~1985
8405393	50432359	8	~1986
8405711	16811423	8	~1985
8405843	16811687	8	~1985
8406059	67248473	8	~1987
8406287	201750889	9	~1988
8406367	201752809	9	~1988
8406479	16812959	8	~1985
8406539	67252313	8	~1987
8406773	50440639	8	~1986
8406817	50440903	8	~1986
8406919	84069191	8	~1987
8407331	16814663	8	~1985
8407331	67258649	8
8407757	67262057	8	~1987
8407957	50447743	8	~1986
8407967	67263737	8	~1987
8408111	16816223	8	~1985
8408237	50449423	8	~1986
8408297	50449783	8	~1986
8408461	134535377	9	~1987
8408549	67268393	8	~1987

5.187.277 digits

25-11-17