Small Mersenne Prime Factors (page 946/5460)

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
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

Exp.	Prime Factor	Digits	Year
8408663	16817327	8	~1985
8409041	67272329	8	~1987
8409239	16818479	8	~1985
8409491	16818983	8	~1985
8409671	16819343	8	~1985
8409719	67277753	8	~1987
8409839	67278713	8	~1987
8410079	16820159	8	~1985
8410139	67281113	8	~1987
8410151	16820303	8	~1985
8410151	67281209	8
8410397	117745559	9	~1987
8410537	50463223	8	~1986
8410679	16821359	8	~1985
8410691	16821383	8	~1985
8410739	67285913	8	~1987
8410793	50464759	8	~1986
8410799	16821599	8	~1985
8410859	16821719	8	~1985
8410943	16821887	8	~1985
8410991	16821983	8	~1985
8411071	84110711	8	~1987
8411171	16822343	8	~1985
8411233	50467399	8	~1986
8411521	50469127	8	~1986

Exp.	Prime Factor	Digits	Year
8411621	925278311	9	~1989
8411681	50470087	8	~1986
8411723	16823447	8	~1985
8412077	50472463	8	~1986
8412119	16824239	8	~1985
8412251	16824503	8	~1985
8412311	16824623	8	~1985
8412317	67298537	8	~1987
8412527	67300217	8	~1987
8412539	16825079	8	~1985
8412793	50476759	8	~1986
8413001	50478007	8	~1986
8413109	67304873	8	~1987
8413271	16826543	8	~1985
8413403	16826807	8	~1985
8413439	16826879	8	~1985
8413439	353364439	9
8413661	50481967	8	~1986
8413661	67309289	8
8413687	336547481	9	~1988
8413721	67309769	8	~1987
8413781	67310249	8	~1987
8413841	67310729	8	~1987
8414117	50484703	8	~1986
8414233	50485399	8	~1986

Exp.	Prime Factor	Digits	Year
8414537	50487223	8	~1986
8414557	50487343	8	~1986
8414647	84146471	8	~1987
8415241	50491447	8	~1986
8415359	16830719	8	~1985
8415503	16831007	8	~1985
8415703	134651249	9	~1987
8415941	67327529	8	~1987
8416171	134658737	9	~1987
8416267	84162671	8	~1987
8416301	50497807	8	~1986
8416393	50498359	8	~1986
8416403	16832807	8	~1985
8416451	16832903	8	~1985
8416451	67331609	8
8416511	16833023	8	~1985
8416621	50499727	8	~1986
8416817	1885367009	10	~1990
8417063	16834127	8	~1985
8417231	16834463	8	~1985
8417231	67337849	8
8417681	50506087	8	~1986
8417711	67341689	8	~1987
8418013	50508079	8	~1986
8418359	16836719	8	~1985

5.157.210 digits

25-11-02