Small Mersenne Prime Factors (page 1034/5985)

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
9286523	18573047	8	~1985
9286631	18573263	8	~1985
9286817	74294537	8	~1987
9286831	92868311	8	~1987
9287053	55722319	8	~1987
9287081	55722487	8	~1987
9287123	18574247	8	~1985
9287231	18574463	8	~1985
9287231	74297849	8
9287237	74297897	8	~1987
9287483	18574967	8	~1985
9287651	18575303	8	~1985
9288271	92882711	8	~1987
9288361	55730167	8	~1987
9288413	278652391	9	~1988
9288557	352965167	9	~1989
9288599	18577199	8	~1985
9288659	18577319	8	~1985
9288857	55733143	8	~1987
9288971	18577943	8	~1985
9289211	18578423	8	~1985
9289417	55736503	8	~1987
9289433	55736599	8	~1987
9289523	18579047	8	~1985
9289523	222948553	9

Exp.	Prime Factor	Digits	Year
9289807	148636913	9	~1988
9289817	74318537	8	~1987
9289979	18579959	8	~1985
9289991	18579983	8	~1985
9290003	18580007	8	~1985
9290129	74321033	8	~1987
9290399	18580799	8	~1985
9290591	74324729	8	~1987
9291013	204402287	9	~1988
9291083	18582167	8	~1985
9291251	18582503	8	~1985
9291481	55748887	8	~1987
9291539	18583079	8	~1985
9291613	55749679	8	~1987
9292037	55752223	8	~1987
9292091	18584183	8	~1985
9292541	55755247	8	~1987
9292553	55755319	8	~1987
9293171	18586343	8	~1985
9293243	18586487	8	~1985
9293483	223043593	9	~1988
9293519	18587039	8	~1985
9293579	18587159	8	~1985
9293657	74349257	8	~1987
9294193	55765159	8	~1987

Exp.	Prime Factor	Digits	Year
9294421	55766527	8	~1987
9294521	74356169	8	~1987
9294611	18589223	8	~1985
9294697	55768183	8	~1987
9294793	55768759	8	~1987
9294941	55769647	8	~1987
9294959	18589919	8	~1985
9295043	18590087	8	~1985
9295619	18591239	8	~1985
9295679	18591359	8	~1985
9295681	55774087	8	~1987
9295823	18591647	8	~1985
9295901	55775407	8	~1987
9295963	92959631	8	~1987
9296033	55776199	8	~1987
9296123	18592247	8	~1985
9296351	18592703	8	~1985
9296579	74372633	8	~1987
9296839	92968391	8	~1987
9296981	74375849	8	~1987
9297053	55782319	8	~1987
9297143	18594287	8	~1985
9297311	18594623	8	~1985
9297377	55784263	8	~1987
9297461	55784767	8	~1987

Exp.	Prime Factor	Digits	Year
9297461	74379689	8
9297599	74380793	8	~1987
9297731	18595463	8	~1985
9297853	204552767	9	~1988
9297887	167361967	9	~1988
9298043	18596087	8	~1985
9298259	18596519	8	~1985
9298301	74386409	8	~1987
9298397	130177559	9	~1988
9298829	74390633	8	~1987
9298889	74391113	8	~1987
9299161	55794967	8	~1987
9299161	278974831	9
9299161	669539593	9
9299197	55795183	8	~1987
9299219	18598439	8	~1985
9299243	18598487	8	~1985
9299351	18598703	8	~1985
9299369	130191167	9	~1988
9300023	18600047	8	~1985
9300143	18600287	8	~1985
9300301	55801807	8	~1987
9300359	18600719	8	~1985
9300719	18601439	8	~1985
9300719	167412943	9

5.680.769 digits

26-07-05