Small Mersenne Prime Factors (page 707/5025)

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
5371631	10743263	8	~1984
5371739	96691303	8	~1986
5371879	182643887	9	~1987
5372099	10744199	8	~1984
5372177	75210479	8	~1986
5372309	42978473	8	~1985
5372413	32234479	8	~1985
5372519	10745039	8	~1984
5372597	32235583	8	~1985
5372723	10745447	8	~1984
5372771	10745543	8	~1984
5372831	10745663	8	~1984
5372933	32237599	8	~1985
5373239	10746479	8	~1984
5373383	10746767	8	~1984
5373611	10747223	8	~1984
5373611	42988889	8
5373791	42990329	8	~1985
5373857	32243143	8	~1985
5373857	806078551	9
5374079	10748159	8	~1984
5374151	10748303	8	~1984
5374459	128987017	9	~1986
5374517	161235511	9	~1986
5374661	42997289	8	~1985

Exp.	Prime Factor	Digits	Year
5374693	32248159	8	~1985
5374951	53749511	8	~1985
5375443	53754431	8	~1985
5375683	53756831	8	~1985
5375707	53757071	8	~1985
5375761	32254567	8	~1985
5376011	10752023	8	~1984
5376023	10752047	8	~1984
5376083	10752167	8	~1984
5376251	10752503	8	~1984
5376323	10752647	8	~1984
5376353	32258119	8	~1985
5376389	258066673	9	~1987
5376443	10752887	8	~1984
5376551	10753103	8	~1984
5377103	10754207	8	~1984
5377153	129051673	9	~1986
5377237	32263423	8	~1985
5377343	139810919	9	~1986
5377417	32264503	8	~1985
5377439	10754879	8	~1984
5377657	32265943	8	~1985
5377679	10755359	8	~1984
5377907	516279073	9	~1988
5377919	225872599	9	~1987

Exp.	Prime Factor	Digits	Year
5378207	96807727	8	~1986
5378677	129088249	9	~1986
5378731	53787311	8	~1985
5378993	32273959	8	~1985
5379113	32274679	8	~1985
5379251	96826519	8	~1986
5379281	43034249	8	~1985
5379359	10758719	8	~1984
5379431	139865207	9	~1986
5379533	32277199	8	~1985
5379611	10759223	8	~1984
5379637	32277823	8	~1985
5380237	32281423	8	~1985
5380351	86085617	8	~1986
5380423	182934383	9	~1987
5380499	43043993	8	~1985
5380691	10761383	8	~1984
5380883	10761767	8	~1984
5380937	32285623	8	~1985
5380943	10761887	8	~1984
5381093	75335303	8	~1986
5381377	129153049	9	~1986
5381581	32289487	8	~1985
5381819	10763639	8	~1984
5381939	96874903	8	~1986

Exp.	Prime Factor	Digits	Year
5381951	10763903	8	~1984
5382107	43056857	8	~1985
5382119	43056953	8	~1985
5382233	32293399	8	~1985
5382691	86123057	8	~1986
5382991	53829911	8	~1985
5383151	10766303	8	~1984
5383361	43066889	8	~1985
5383787	43070297	8	~1985
5383949	2228954887	10	~1989
5384063	10768127	8	~1984
5384303	10768607	8	~1984
5384383	53843831	8	~1985
5384471	10768943	8	~1984
5384501	32307007	8	~1985
5384671	53846711	8	~1985
5385593	32313559	8	~1985
5385839	10771679	8	~1984
5385839	43086713	8
5386103	10772207	8	~1984
5386769	560223977	9	~1988
5386891	86190257	8	~1986
5386993	32321959	8	~1985
5387071	53870711	8	~1985
5387111	10774223	8	~1984

4.724.182 digits

25-04-13