Small Mersenne Prime Factors (page 561/5850)

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
3406687	34066871	8	~1984
3406939	34069391	8	~1984
3406943	6813887	7	~1982
3406973	735906169	9	~1987
3407207	88587383	8	~1985
3407333	20443999	8	~1983
3407597	163564657	9	~1985
3407659	163567633	9	~1985
3407773	54524369	8	~1984
3407977	81791449	8	~1985
3408001	20448007	8	~1983
3408263	6816527	7	~1982
3408319	34083191	8	~1984
3408343	34083431	8	~1984
3408413	47717783	8	~1984
3408437	20450623	8	~1983
3408437	47718119	8
3408473	20450839	8	~1983
3408479	81803497	8	~1985
3408511	54536177	8	~1984
3408533	20451199	8	~1983
3408599	27268793	8	~1984
3408659	6817319	7	~1982
3408719	61356943	8	~1984
3408787	34087871	8	~1984

Exp.	Prime Factor	Digits	Year
3409093	20454559	8	~1983
3409141	300004409	9	~1986
3409223	6818447	7	~1982
3409247	354561689	9	~1986
3409261	75003743	8	~1985
3409321	20455927	8	~1983
3409583	88649159	8	~1985
3409591	34095911	8	~1984
3409751	6819503	7	~1982
3409789	75015359	8	~1985
3409811	6819623	7	~1982
3409853	20459119	8	~1983
3409853	511477951	9
3410009	265980703	9	~1986
3410051	6820103	7	~1982
3410089	102302671	9	~1985
3410131	34101311	8	~1984
3410249	27281993	8	~1984
3410369	27282953	8	~1984
3410783	6821567	7	~1982
3410857	20465143	8	~1983
3411049	81865177	8	~1985
3411311	6822623	7	~1982
3411523	34115231	8	~1984
3411599	6823199	7	~1982

Exp.	Prime Factor	Digits	Year
3411673	20470039	8	~1983
3411701	163761649	9	~1985
3411739	61411303	8	~1984
3411851	6823703	7	~1982
3411893	47766503	8	~1984
3411901	156947447	9	~1985
3412067	580051391	9	~1987
3412069	75065519	8	~1985
3412309	75070799	8	~1985
3412313	20473879	8	~1983
3412481	109199393	9	~1985
3412483	81899593	8	~1985
3412537	218402369	9	~1986
3412583	6825167	7	~1982
3412637	27301097	8	~1984
3412649	27301193	8	~1984
3412679	6825359	7	~1982
3412679	27301433	8
3412753	566516999	9	~1987
3412931	27303449	8	~1984
3412949	27303593	8	~1984
3413051	6826103	7	~1982
3413077	20478463	8	~1983
3413099	27304793	8	~1984
3413101	20478607	8	~1983

Exp.	Prime Factor	Digits	Year
3413411	6826823	7	~1982
3413759	6827519	7	~1982
3413789	47793047	8	~1984
3413831	27310649	8	~1984
3414011	6828023	7	~1982
3414163	34141631	8	~1984
3414227	27313817	8	~1984
3414287	27314297	8	~1984
3414311	6828623	7	~1982
3414337	20486023	8	~1983
3414421	20486527	8	~1983
3414457	20486743	8	~1983
3414457	102433711	9
3414527	61461487	8	~1984
3414581	20487487	8	~1983
3414857	81956569	8	~1985
3414883	34148831	8	~1984
3415261	20491567	8	~1983
3415679	6831359	7	~1982
3415697	20494183	8	~1983
3415697	27325577	8
3415757	20494543	8	~1983
3415781	27326249	8	~1984
3415883	6831767	7	~1982
3415897	20495383	8	~1983

5.546.121 digits

26-05-03