Small Mersenne Prime Factors (page 946/5745)

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
8177849	65422793	8	~1986
8178007	81780071	8	~1987
8178077	65424617	8	~1986
8178217	245346511	9	~1988
8178293	49069759	8	~1986
8178473	49070839	8	~1986
8178481	49070887	8	~1986
8178617	49071703	8	~1986
8178707	65429657	8	~1986
8178743	16357487	8	~1985
8178839	65430713	8	~1986
8178959	16357919	8	~1985
8178959	65431673	8
8179019	16358039	8	~1985
8179103	16358207	8	~1985
8179201	49075207	8	~1986
8179343	16358687	8	~1985
8179403	16358807	8	~1985
8179511	16359023	8	~1985
8179631	16359263	8	~1985
8179751	343549543	9	~1988
8180041	130880657	9	~1987
8180041	179960903	9
8180239	147244303	9	~1987
8180423	16360847	8	~1985

Exp.	Prime Factor	Digits	Year
8180531	16361063	8	~1985
8180713	49084279	8	~1986
8180759	16361519	8	~1985
8180857	49085143	8	~1986
8181053	49086319	8	~1986
8181127	81811271	8	~1987
8181317	65450537	8	~1986
8181359	16362719	8	~1985
8181623	16363247	8	~1985
8181731	16363463	8	~1985
8181851	16363703	8	~1985
8181949	441825247	9	~1988
8182121	49092727	8	~1986
8182123	130913969	9	~1987
8182157	49092943	8	~1986
8182387	81823871	8	~1987
8182417	49094503	8	~1986
8182709	65461673	8	~1986
8182897	49097383	8	~1986
8183293	49099759	8	~1986
8183297	196399129	9	~1988
8183317	49099903	8	~1986
8183369	65466953	8	~1986
8183603	16367207	8	~1985
8183621	65468969	8	~1986

Exp.	Prime Factor	Digits	Year
8183711	16367423	8	~1985
8183761	49102567	8	~1986
8183933	114575063	9	~1987
8184301	49105807	8	~1986
8184359	16368719	8	~1985
8184443	16368887	8	~1985
8184581	311014079	9	~1988
8184773	49108639	8	~1986
8184779	16369559	8	~1985
8184971	16369943	8	~1985
8185031	16370063	8	~1985
8185283	16370567	8	~1985
8185301	65482409	8	~1986
8185421	49112527	8	~1986
8185451	16370903	8	~1985
8185469	114596567	9	~1987
8185649	65485193	8	~1986
8185657	49113943	8	~1986
8185799	16371599	8	~1985
8185981	49115887	8	~1986
8186099	16372199	8	~1985
8186219	16372439	8	~1985
8186351	16372703	8	~1985
8186411	16372823	8	~1985
8186603	16373207	8	~1985

Exp.	Prime Factor	Digits	Year
8186621	49119727	8	~1986
8186831	16373663	8	~1985
8186861	49121167	8	~1986
8186933	49121599	8	~1986
8187031	81870311	8	~1987
8187089	65496713	8	~1986
8187197	65497577	8	~1986
8187337	1031604463	10	~1989
8187373	49124239	8	~1986
8187539	65500313	8	~1986
8187719	16375439	8	~1985
8187719	65501753	8
8187743	16375487	8	~1985
8188163	262021217	9	~1988
8188547	147393847	9	~1987
8188613	49131679	8	~1986
8188693	180151247	9	~1988
8189227	147406087	9	~1987
8189453	49136719	8	~1986
8189593	49137559	8	~1986
8189663	16379327	8	~1985
8189681	49138087	8	~1986
8189777	65518217	8	~1986
8189939	16379879	8	~1985
8189963	16379927	8	~1985

5.441.361 digits

26-03-15