Small Mersenne Prime Factors (page 977/5205)

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
9171731	18343463	8	~1985
9171881	55031287	8	~1987
9171907	91719071	8	~1987
9171971	18343943	8	~1985
9172057	495291079	9	~1989
9172133	55032799	8	~1987
9172211	18344423	8	~1985
9172343	18344687	8	~1985
9172451	18344903	8	~1985
9172463	18344927	8	~1985
9172739	18345479	8	~1985
9173093	55038559	8	~1987
9173273	55039639	8	~1987
9173291	18346583	8	~1985
9173377	55040263	8	~1987
9173459	18346919	8	~1985
9174197	55045183	8	~1987
9174299	18348599	8	~1985
9174383	18348767	8	~1985
9174521	55047127	8	~1987
9174563	18349127	8	~1985
9174601	55047607	8	~1987
9174647	165143647	9	~1988
9174719	18349439	8	~1985
9174839	18349679	8	~1985

Exp.	Prime Factor	Digits	Year
9174983	18349967	8	~1985
9175337	73402697	8	~1987
9175457	73403657	8	~1987
9175871	18351743	8	~1985
9175913	55055479	8	~1987
9176003	220224073	9	~1988
9176017	55056103	8	~1987
9176023	91760231	8	~1987
9176099	18352199	8	~1985
9176543	18353087	8	~1985
9176599	660715129	9	~1989
9176803	91768031	8	~1987
9177293	55063759	8	~1987
9177373	55064239	8	~1987
9177491	18354983	8	~1985
9177599	18355199	8	~1985
9177617	73420937	8	~1987
9177733	660796777	9	~1989
9178231	13216652641	11	~1992
9178451	18356903	8	~1985
9178751	18357503	8	~1985
9178751	73430009	8
9178979	18357959	8	~1985
9179029	1028051249	10	~1990
9179111	73432889	8	~1987

Exp.	Prime Factor	Digits	Year
9179153	55074919	8	~1987
9179693	55078159	8	~1987
9180071	18360143	8	~1985
9180191	18360383	8	~1985
9180299	18360599	8	~1985
9180383	18360767	8	~1985
9180659	18361319	8	~1985
9180767	165253807	9	~1988
9181129	275433871	9	~1988
9181261	55087567	8	~1987
9181391	18362783	8	~1985
9181619	18363239	8	~1985
9181631	18363263	8	~1985
9181657	55089943	8	~1987
9182171	18364343	8	~1985
9182233	146915729	9	~1988
9182627	220383049	9	~1988
9182639	18365279	8	~1985
9183131	18366263	8	~1985
9183373	55100239	8	~1987
9183641	55101847	8	~1987
9183653	128571143	9	~1987
9183793	55102759	8	~1987
9183841	55103047	8	~1987
9184027	165312487	9	~1988

Exp.	Prime Factor	Digits	Year
9184093	55104559	8	~1987
9184477	25404263383	11	~1993
9184537	55107223	8	~1987
9185153	55110919	8	~1987
9185171	18370343	8	~1985
9185339	18370679	8	~1985
9185399	18370799	8	~1985
9185723	18371447	8	~1985
9185741	55114447	8	~1987
9185881	55115287	8	~1987
9186053	55116319	8	~1987
9186263	18372527	8	~1985
9187103	18374207	8	~1985
9187163	18374327	8	~1985
9187313	55123879	8	~1987
9187333	146997329	9	~1988
9187457	55124743	8	~1987
9187933	55127599	8	~1987
9187993	55127959	8	~1987
9188021	73504169	8	~1987
9188303	18376607	8	~1985
9188351	18376703	8	~1985
9188897	73511177	8	~1987
9189023	18378047	8	~1985
9189071	165403279	9	~1988

4.903.097 digits

25-07-08