Small Mersenne Prime Factors (page 910/5670)

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
7700639	15401279	8	~1985
7700717	61605737	8	~1986
7700753	46204519	8	~1986
7700831	15401663	8	~1985
7701131	15402263	8	~1985
7701623	15403247	8	~1985
7701721	677751449	9	~1989
7701817	46210903	8	~1986
7701847	123229553	9	~1987
7701977	46211863	8	~1986
7702199	15404399	8	~1985
7702271	61618169	8	~1986
7702379	15404759	8	~1985
7702433	46214599	8	~1986
7702451	15404903	8	~1985
7702451	61619609	8
7702511	15405023	8	~1985
7702763	15405527	8	~1985
7702811	15405623	8	~1985
7703309	61626473	8	~1986
7703609	61628873	8	~1986
7703621	61628969	8	~1986
7703671	77036711	8	~1986
7703963	15407927	8	~1985
7704071	15408143	8	~1985

Exp.	Prime Factor	Digits	Year
7704083	15408167	8	~1985
7704217	46225303	8	~1986
7704331	77043311	8	~1986
7704449	61635593	8	~1986
7704457	46226743	8	~1986
7704803	15409607	8	~1985
7704841	46229047	8	~1986
7704913	46229479	8	~1986
7705031	15410063	8	~1985
7705079	61640633	8	~1986
7705283	15410567	8	~1985
7705601	61644809	8	~1986
7705937	107883119	9	~1987
7706063	15412127	8	~1985
7706119	77061191	8	~1986
7706459	15412919	8	~1985
7706561	431567417	9	~1988
7706717	46240303	8	~1986
7706719	77067191	8	~1986
7706753	231202591	9	~1988
7706843	15413687	8	~1985
7707053	46242319	8	~1986
7707269	184974457	9	~1987
7707587	184982089	9	~1987
7707797	292896287	9	~1988

Exp.	Prime Factor	Digits	Year
7707923	15415847	8	~1985
7708397	107917559	9	~1987
7709033	46254199	8	~1986
7709063	15418127	8	~1985
7709153	46254919	8	~1986
7709227	123347633	9	~1987
7709587	77095871	8	~1987
7709699	15419399	8	~1985
7709813	107937383	9	~1987
7710007	138780127	9	~1987
7710377	46262263	8	~1986
7710743	15421487	8	~1985
7710863	15421727	8	~1985
7711019	61688153	8	~1986
7711057	46266343	8	~1986
7711087	77110871	8	~1987
7711103	15422207	8	~1985
7711139	15422279	8	~1985
7711181	46267087	8	~1986
7711469	61691753	8	~1986
7711573	46269439	8	~1986
7711933	416444383	9	~1988
7712051	61696409	8	~1986
7712213	107970983	9	~1987
7712219	15424439	8	~1985

Exp.	Prime Factor	Digits	Year
7712729	61701833	8	~1986
7712819	15425639	8	~1985
7713071	15426143	8	~1985
7713071	61704569	8
7713077	107983079	9	~1987
7713127	308525081	9	~1988
7713569	61708553	8	~1986
7713613	46281679	8	~1986
7713659	246837089	9	~1988
7713701	46282207	8	~1986
7714111	77141111	8	~1987
7714571	15429143	8	~1985
7714621	46287727	8	~1986
7714757	61718057	8	~1986
7714921	231447631	9	~1988
7715053	46290319	8	~1986
7715423	15430847	8	~1985
7715549	108017687	9	~1987
7715579	15431159	8	~1985
7715723	15431447	8	~1985
7715891	15431783	8	~1985
7715959	77159591	8	~1987
7716019	77160191	8	~1987
7716281	46297687	8	~1986
7716503	15433007	8	~1985

5.366.787 digits

26-02-08