Small Mersenne Prime Factors (page 762/5025)

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
6085897	36515383	8	~1985
6086057	36516343	8	~1985
6086243	12172487	8	~1984
6086471	12172943	8	~1984
6086497	36518983	8	~1985
6086503	60865031	8	~1986
6086543	12173087	8	~1984
6086623	255638167	9	~1987
6086747	48693977	8	~1985
6086903	12173807	8	~1984
6087401	36524407	8	~1985
6087451	60874511	8	~1986
6087973	36527839	8	~1985
6088087	60880871	8	~1986
6088099	109585783	9	~1986
6088343	12176687	8	~1984
6088457	36530743	8	~1985
6088457	48707657	8
6088561	36531367	8	~1985
6088739	12177479	8	~1984
6088847	48710777	8	~1985
6088937	85245119	8	~1986
6088937	340980473	9
6089243	146141833	9	~1987
6089351	12178703	8	~1984

Exp.	Prime Factor	Digits	Year
6089471	158326247	9	~1987
6089539	1120475177	10	~1989
6089543	12179087	8	~1984
6089591	12179183	8	~1984
6089597	36537583	8	~1985
6089651	12179303	8	~1984
6090121	243604841	9	~1987
6090137	48721097	8	~1985
6090173	36541039	8	~1985
6090251	12180503	8	~1984
6090299	12180599	8	~1984
6090373	97445969	8	~1986
6090671	12181343	8	~1984
6090739	60907391	8	~1986
6090803	12181607	8	~1984
6090923	12181847	8	~1984
6090941	48727529	8	~1985
6091031	12182063	8	~1984
6091357	36548143	8	~1985
6091451	12182903	8	~1984
6091511	12183023	8	~1984
6091541	1644716071	10	~1989
6091741	36550447	8	~1985
6092123	12184247	8	~1984
6092173	36553039	8	~1985

Exp.	Prime Factor	Digits	Year
6092249	85291487	8	~1986
6092287	60922871	8	~1986
6092311	60923111	8	~1986
6092357	36554143	8	~1985
6092441	182773231	9	~1987
6092561	36555367	8	~1985
6092591	12185183	8	~1984
6092701	36556207	8	~1985
6092959	60929591	8	~1986
6093011	12186023	8	~1984
6093179	12186359	8	~1984
6093223	60932231	8	~1986
6093337	36560023	8	~1985
6093671	255934183	9	~1987
6093853	36563119	8	~1985
6093869	85314167	8	~1986
6093881	48751049	8	~1985
6093931	60939311	8	~1986
6094217	36565303	8	~1985
6094481	48755849	8	~1985
6094567	60945671	8	~1986
6095339	48762713	8	~1985
6095543	12191087	8	~1984
6095647	97530353	8	~1986
6095729	48765833	8	~1985

Exp.	Prime Factor	Digits	Year
6095767	60957671	8	~1986
6095777	36574663	8	~1985
6095891	12191783	8	~1984
6095917	36575503	8	~1985
6095951	12191903	8	~1984
6096071	12192143	8	~1984
6096137	36576823	8	~1985
6096437	36578623	8	~1985
6096661	36579967	8	~1985
6096683	12193367	8	~1984
6096809	85355327	8	~1986
6096997	182909911	9	~1987
6097103	12194207	8	~1984
6097121	48776969	8	~1985
6097213	36583279	8	~1985
6097241	36583447	8	~1985
6097241	48777929	8
6097313	36583879	8	~1985
6097331	48778649	8	~1985
6097439	48779513	8	~1985
6097463	12194927	8	~1984
6097631	12195263	8	~1984
6098017	36588103	8	~1985
6098171	12196343	8	~1984
6098237	85375319	8	~1986

4.724.182 digits

25-04-13