Small Mersenne Prime Factors (page 949/5610)

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
8330789	66646313	8	~1987
8330963	16661927	8	~1985
8330999	16661999	8	~1985
8331097	399892657	9	~1988
8331131	16662263	8	~1985
8331181	49987087	8	~1986
8331371	16662743	8	~1985
8331571	149968279	9	~1987
8331599	349927159	9	~1988
8331857	49991143	8	~1986
8331923	16663847	8	~1985
8332223	16664447	8	~1985
8332277	49993663	8	~1986
8332361	49994167	8	~1986
8332403	16664807	8	~1985
8332777	49996663	8	~1986
8333183	16666367	8	~1985
8333651	16667303	8	~1985
8333779	200010697	9	~1988
8333861	50003167	8	~1986
8333999	16667999	8	~1985
8334101	50004607	8	~1986
8334323	16668647	8	~1985
8334343	83343431	8	~1987
8334377	50006263	8	~1986

Exp.	Prime Factor	Digits	Year
8334527	66676217	8	~1987
8334779	16669559	8	~1985
8334899	16669799	8	~1985
8334929	66679433	8	~1987
8335031	16670063	8	~1985
8335073	50010439	8	~1986
8335157	50010943	8	~1986
8335273	50011639	8	~1986
8335583	16671167	8	~1985
8335643	16671287	8	~1985
8335991	16671983	8	~1985
8336147	66689177	8	~1987
8336677	50020063	8	~1986
8336873	50021239	8	~1986
8337137	66697097	8	~1987
8337149	66697193	8	~1987
8337457	133399313	9	~1987
8337611	16675223	8	~1985
8337653	50025919	8	~1986
8337863	16675727	8	~1985
8338049	250141471	9	~1988
8338091	16676183	8	~1985
8338103	16676207	8	~1985
8338139	16676279	8	~1985
8338247	416912351	9	~1988

Exp.	Prime Factor	Digits	Year
8338751	16677503	8	~1985
8338933	250167991	9	~1988
8338943	16677887	8	~1985
8339057	50034343	8	~1986
8339339	16678679	8	~1985
8339657	50037943	8	~1986
8339657	66717257	8
8339677	50038063	8	~1986
8339711	16679423	8	~1985
8339711	150114799	9
8339909	316916543	9	~1988
8340119	16680239	8	~1985
8340533	50043199	8	~1986
8340817	50044903	8	~1986
8340851	16681703	8	~1985
8340911	16681823	8	~1985
8341187	150141367	9	~1987
8341397	66731177	8	~1987
8341451	16682903	8	~1985
8341499	16682999	8	~1985
8341523	16683047	8	~1985
8341601	50049607	8	~1986
8341657	50049943	8	~1986
8342051	16684103	8	~1985
8342303	16684607	8	~1985

Exp.	Prime Factor	Digits	Year
8342519	66740153	8	~1987
8342759	16685519	8	~1985
8342779	150170023	9	~1987
8342839	83428391	8	~1987
8342857	200228569	9	~1988
8342861	66742889	8	~1987
8343037	50058223	8	~1986
8343059	16686119	8	~1985
8343239	16686479	8	~1985
8343373	50060239	8	~1986
8343383	16686767	8	~1985
8343407	66747257	8	~1987
8343899	16687799	8	~1985
8343899	66751193	8
8344157	66753257	8	~1987
8344621	50067727	8	~1986
8344631	16689263	8	~1985
8344681	50068087	8	~1986
8344799	16689599	8	~1985
8344811	16689623	8	~1985
8345101	50070607	8	~1986
8345171	16690343	8	~1985
8345279	16690559	8	~1985
8345321	66762569	8	~1987
8345377	50072263	8	~1986

5.307.017 digits

26-01-11