Small Mersenne Prime Factors (page 924/5790)

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
7809533	46857199	8	~1986
7809601	46857607	8	~1986
7809757	46858543	8	~1986
7809793	46858759	8	~1986
7809821	62478569	8	~1986
7809911	15619823	8	~1985
7810057	46860343	8	~1986
7810183	78101831	8	~1987
7810333	187447993	9	~1987
7810421	46862527	8	~1986
7810619	15621239	8	~1985
7810721	46864327	8	~1986
7810739	15621479	8	~1985
7810931	15621863	8	~1985
7810987	124975793	9	~1987
7811057	46866343	8	~1986
7811173	46867039	8	~1986
7811203	124979249	9	~1987
7811543	15623087	8	~1985
7811561	62492489	8	~1986
7811663	515569759	9	~1989
7811879	15623759	8	~1985
7812071	15624143	8	~1985
7812121	171866663	9	~1987
7812179	62497433	8	~1986

Exp.	Prime Factor	Digits	Year
7812599	15625199	8	~1985
7813037	62504297	8	~1986
7813109	62504873	8	~1986
7813241	46879447	8	~1986
7813343	15626687	8	~1985
7813451	15626903	8	~1985
7813801	46882807	8	~1986
7813853	46883119	8	~1986
7813979	15627959	8	~1985
7814413	46886479	8	~1986
7814783	15629567	8	~1985
7814819	15629639	8	~1985
7814837	46889023	8	~1986
7814843	15629687	8	~1985
7815281	62522249	8	~1986
7815397	46892383	8	~1986
7815629	62525033	8	~1986
7815737	46894423	8	~1986
7815793	46894759	8	~1986
7816271	15632543	8	~1985
7816463	15632927	8	~1985
7816513	46899079	8	~1986
7816513	312660521	9
7816541	46899247	8	~1986
7816541	62532329	8

Exp.	Prime Factor	Digits	Year
7816643	15633287	8	~1985
7816759	78167591	8	~1987
7817219	15634439	8	~1985
7817233	46903399	8	~1986
7817311	78173111	8	~1987
7817423	15634847	8	~1985
7817609	62540873	8	~1986
7817963	15635927	8	~1985
7818001	46908007	8	~1986
7818731	15637463	8	~1985
7819153	46914919	8	~1986
7819193	46915159	8	~1986
7819271	15638543	8	~1985
7819391	15638783	8	~1985
7819457	109472399	9	~1987
7819631	15639263	8	~1985
7820159	15640319	8	~1985
7820303	15640607	8	~1985
7820591	15641183	8	~1985
7820639	15641279	8	~1985
7820803	328473727	9	~1988
7821059	15642119	8	~1985
7821299	62570393	8	~1986
7821323	15642647	8	~1985
7821371	15642743	8	~1985

Exp.	Prime Factor	Digits	Year
7821791	15643583	8	~1985
7821991	140795839	9	~1987
7822019	15644039	8	~1985
7822379	391118951	9	~1988
7822769	62582153	8	~1986
7822931	15645863	8	~1985
7822931	62583449	8
7823017	46938103	8	~1986
7823143	125170289	9	~1987
7823239	78232391	8	~1987
7823279	15646559	8	~1985
7823603	15647207	8	~1985
7823759	15647519	8	~1985
7823951	62591609	8	~1986
7824107	62592857	8	~1986
7824203	15648407	8	~1985
7824277	46945663	8	~1986
7824497	46946983	8	~1986
7824497	62595977	8
7824673	359934959	9	~1988
7824731	62597849	8	~1986
7824923	15649847	8	~1985
7825327	78253271	8	~1987
7825421	62603369	8	~1986
7825529	62604233	8	~1986

5.486.313 digits

26-04-05