Small Mersenne Prime Factors (page 941/5205)

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
8563283	17126567	8	~1985
8563517	68508137	8	~1987
8563559	17127119	8	~1985
8563741	51382447	8	~1986
8563811	17127623	8	~1985
8564063	17128127	8	~1985
8564113	256923391	9	~1988
8564123	17128247	8	~1985
8564273	51385639	8	~1986
8564813	51388879	8	~1986
8565281	51391687	8	~1986
8565581	68524649	8	~1987
8565691	85656911	8	~1987
8565971	17131943	8	~1985
8566021	51396127	8	~1986
8566319	17132639	8	~1985
8566451	17132903	8	~1985
8566469	68531753	8	~1987
8566559	17133119	8	~1985
8566703	17133407	8	~1985
8566823	17133647	8	~1985
8567203	137075249	9	~1987
8567591	68540729	8	~1987
8568011	17136023	8	~1985
8568179	17136359	8	~1985

Exp.	Prime Factor	Digits	Year
8568611	17137223	8	~1985
8568773	51412639	8	~1986
8568961	137103377	9	~1987
8568979	154241623	9	~1987
8569031	17138063	8	~1985
8569321	599852471	9	~1989
8569441	51416647	8	~1986
8569493	119972903	9	~1987
8569559	17139119	8	~1985
8569637	51417823	8	~1986
8569679	17139359	8	~1985
8569763	359930047	9	~1988
8569937	68559497	8	~1987
8569987	85699871	8	~1987
8570137	51420823	8	~1986
8570279	17140559	8	~1985
8570357	51422143	8	~1986
8570647	85706471	8	~1987
8571067	154279207	9	~1987
8571271	154282879	9	~1987
8571361	137141777	9	~1987
8571401	51428407	8	~1986
8571803	222866879	9	~1988
8571811	85718111	8	~1987
8571973	51431839	8	~1986

Exp.	Prime Factor	Digits	Year
8572141	51432847	8	~1986
8572229	120011207	9	~1987
8572331	17144663	8	~1985
8572541	1971684431	10	~1990
8572643	17145287	8	~1985
8572693	822978529	9	~1989
8572727	68581817	8	~1987
8572853	51437119	8	~1986
8572871	17145743	8	~1985
8573393	51440359	8	~1986
8573437	1697540527	10	~1990
8573441	51440647	8	~1986
8573519	68588153	8	~1987
8573843	2006279263	10	~1990
8573849	68590793	8	~1987
8574403	291529703	9	~1988
8574437	68595497	8	~1987
8574743	17149487	8	~1985
8574809	68598473	8	~1987
8574857	51449143	8	~1986
8574911	17149823	8	~1985
8574959	17149919	8	~1985
8575117	51450703	8	~1986
8575331	68602649	8	~1987
8575493	51452959	8	~1986

Exp.	Prime Factor	Digits	Year
8575603	85756031	8	~1987
8575649	325874663	9	~1988
8575657	51453943	8	~1986
8575733	51454399	8	~1986
8575751	17151503	8	~1985
8576573	51459439	8	~1986
8576699	17153399	8	~1985
8576851	154383319	9	~1987
8577983	17155967	8	~1985
8578019	17156039	8	~1985
8578093	600466511	9	~1989
8578331	17156663	8	~1985
8578331	411759889	9
8578343	17156687	8	~1985
8578439	17156879	8	~1985
8578571	17157143	8	~1985
8578991	17157983	8	~1985
8579111	17158223	8	~1985
8579159	17158319	8	~1985
8579303	17158607	8	~1985
8579531	17159063	8	~1985
8579663	17159327	8	~1985
8579927	223078103	9	~1988
8579999	17159999	8	~1985
8579999	68639993	8

4.903.097 digits

25-07-08