Small Mersenne Prime Factors (page 753/5340)

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
5779063	57790631	8	~1986
5779153	34674919	8	~1985
5779271	11558543	8	~1984
5779331	46234649	8	~1985
5779573	34677439	8	~1985
5779799	11559599	8	~1984
5779843	57798431	8	~1986
5780317	92485073	8	~1986
5780393	34682359	8	~1985
5780711	11561423	8	~1984
5780711	104052799	9
5780923	92494769	8	~1986
5781059	11562119	8	~1984
5781131	11562263	8	~1984
5781239	11562479	8	~1984
5781311	11562623	8	~1984
5781541	127193903	9	~1986
5781749	46253993	8	~1985
5781791	11563583	8	~1984
5781869	173456071	9	~1987
5782043	11564087	8	~1984
5782043	185025377	9
5782043	416307097	9
5782103	11564207	8	~1984
5782163	11564327	8	~1984

Exp.	Prime Factor	Digits	Year
5782391	11564783	8	~1984
5782577	80956079	8	~1986
5782657	34695943	8	~1985
5782951	57829511	8	~1986
5782951	92527217	8
5783153	34698919	8	~1985
5783339	46266713	8	~1985
5783363	11566727	8	~1984
5783369	46266953	8	~1985
5783381	34700287	8	~1985
5783983	92543729	8	~1986
5784089	46272713	8	~1985
5784269	312350527	9	~1987
5784323	11568647	8	~1984
5784421	34706527	8	~1985
5784563	11569127	8	~1984
5784599	46276793	8	~1985
5784673	34708039	8	~1985
5784959	11569919	8	~1984
5785001	46280009	8	~1985
5785337	46282697	8	~1985
5785463	11570927	8	~1984
5785511	11571023	8	~1984
5785589	46284713	8	~1985
5785691	11571383	8	~1984

Exp.	Prime Factor	Digits	Year
5785807	57858071	8	~1986
5785837	173575111	9	~1987
5785859	11571719	8	~1984
5785889	46287113	8	~1985
5785991	11571983	8	~1984
5786281	34717687	8	~1985
5786327	46290617	8	~1985
5786359	57863591	8	~1986
5786369	46290953	8	~1985
5786461	34718767	8	~1985
5786537	46292297	8	~1985
5786861	46294889	8	~1985
5787167	46297337	8	~1985
5787217	34723303	8	~1985
5787851	11575703	8	~1984
5787869	46302953	8	~1985
5788043	11576087	8	~1984
5788193	34729159	8	~1985
5788247	324141833	9	~1987
5788439	11576879	8	~1984
5788457	34730743	8	~1985
5788463	11576927	8	~1984
5788621	34731727	8	~1985
5788793	34732759	8	~1985
5789071	57890711	8	~1986

Exp.	Prime Factor	Digits	Year
5789363	11578727	8	~1984
5789711	11579423	8	~1984
5789779	104216023	9	~1986
5789891	11579783	8	~1984
5789891	46319129	8
5790097	34740583	8	~1985
5790209	220027943	9	~1987
5790419	11580839	8	~1984
5790439	57904391	8	~1986
5790529	138972697	9	~1986
5790539	11581079	8	~1984
5790571	104230279	9	~1986
5790847	57908471	8	~1986
5790847	231633881	9
5790857	34745143	8	~1985
5790899	11581799	8	~1984
5790943	57909431	8	~1986
5791091	11582183	8	~1984
5791109	46328873	8	~1985
5791153	34746919	8	~1985
5791217	81077039	8	~1986
5791231	57912311	8	~1986
5791337	34748023	8	~1985
5791403	11582807	8	~1984
5791463	11582927	8	~1984

5.037.460 digits

25-09-07