Small Mersenne Prime Factors (page 944/4665)

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
9295619	18591239	8	~1985
9295679	18591359	8	~1985
9295681	55774087	8	~1987
9295823	18591647	8	~1985
9295901	55775407	8	~1987
9296033	55776199	8	~1987
9296123	18592247	8	~1985
9296351	18592703	8	~1985
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
9297731	18595463	8	~1985
9297853	204552767	9	~1988
9297887	167361967	9	~1988
9298043	18596087	8	~1985
9298259	18596519	8	~1985
9298397	130177559	9	~1987
9299161	55794967	8	~1987
9299197	55795183	8	~1987
9299219	18598439	8	~1985
9299243	18598487	8	~1985

Exp.	Prime Factor	Digits	Year
9299351	18598703	8	~1985
9299369	130191167	9	~1987
9300023	18600047	8	~1985
9300143	18600287	8	~1985
9300301	55801807	8	~1987
9300359	18600719	8	~1985
9300719	18601439	8	~1985
9300983	18601967	8	~1985
9301139	18602279	8	~1985
9301217	55807303	8	~1987
9301283	18602567	8	~1985
9301673	55810039	8	~1987
9301679	18603359	8	~1985
9301739	18603479	8	~1985
9301807	167432527	9	~1988
9301841	55811047	8	~1987
9301847	74414777	8	~1987
9301931	18603863	8	~1985
9302063	18604127	8	~1985
9302291	18604583	8	~1985
9302483	18604967	8	~1985
9302549	74420393	8	~1987
9302963	18605927	8	~1985
9303181	279095431	9	~1988
9303241	55819447	8	~1987

Exp.	Prime Factor	Digits	Year
9303263	18606527	8	~1985
9303319	93033191	8	~1987
9303377	520989113	9	~1989
9303643	93036431	8	~1987
9303839	18607679	8	~1985
9303851	18607703	8	~1985
9304033	279120991	9	~1988
9304109	74432873	8	~1987
9304271	74434169	8	~1987
9304283	18608567	8	~1985
9304313	55825879	8	~1987
9304511	18609023	8	~1985
9304583	18609167	8	~1985
9304657	55827943	8	~1987
9304931	18609863	8	~1985
9305063	18610127	8	~1985
9305561	55833367	8	~1987
9305771	18611543	8	~1985
9306197	55837183	8	~1987
9306263	18612527	8	~1985
9306383	18612767	8	~1985
9306841	148909457	9	~1988
9307121	55842727	8	~1987
9307121	74456969	8
9307139	18614279	8	~1985

Exp.	Prime Factor	Digits	Year
9307379	18614759	8	~1985
9307997	55847983	8	~1987
9308141	74465129	8	~1987
9308471	18616943	8	~1985
9308513	55851079	8	~1987
9308531	18617063	8	~1985
9308543	18617087	8	~1985
9308557	446810737	9	~1989
9309137	446838577	9	~1989
9309413	130331783	9	~1987
9309479	18618959	8	~1985
9309697	55858183	8	~1987
9310153	55860919	8	~1987
9310241	55861447	8	~1987
9310333	55861999	8	~1987
9310481	55862887	8	~1987
9310523	18621047	8	~1985
9310667	74485337	8	~1987
9310991	18621983	8	~1985
9311063	18622127	8	~1985
9312323	18624647	8	~1985
9312731	18625463	8	~1985
9312767	167629807	9	~1988
9312917	74503337	8	~1987
9313013	55878079	8	~1987

4.368.158 digits

24-10-27