Small Mersenne Prime Factors (page 918/5025)

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
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
8396281	50377687	8	~1986
8396413	50378479	8	~1986
8396761	50380567	8	~1986
8396779	151142023	9	~1987
8396819	67174553	8	~1987
8396953	50381719	8	~1986
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
8399107	83991071	8	~1987
8399401	50396407	8	~1986

Exp.	Prime Factor	Digits	Year
8399621	50397727	8	~1986
8399773	50398639	8	~1986
8400011	16800023	8	~1985
8400061	50400367	8	~1986
8400317	67202537	8	~1987
8400593	50403559	8	~1986
8400731	67205849	8	~1987
8401117	50406703	8	~1986
8401637	50409823	8	~1986
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

Exp.	Prime Factor	Digits	Year
8404283	16808567	8	~1985
8404553	50427319	8	~1986
8404703	16809407	8	~1985
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
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
8408111	16816223	8	~1985
8408237	50449423	8	~1986
8408297	50449783	8	~1986
8408663	16817327	8	~1985

Exp.	Prime Factor	Digits	Year
8409239	16818479	8	~1985
8409491	16818983	8	~1985
8409671	16819343	8	~1985
8409719	67277753	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
8411621	925278311	9	~1989
8411681	50470087	8	~1986
8411723	16823447	8	~1985

4.724.182 digits

25-04-13