Small Mersenne Prime Factors (page 336/5610)

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
1570883	603219073	9	~1985
1570931	3141863	7	~1979
1571027	12568217	8	~1981
1571093	172820231	9	~1984
1571209	37709017	8	~1982
1571239	15712391	8	~1981
1571419	15714191	8	~1981
1571477	12571817	8	~1981
1571579	3143159	7	~1979
1571579	12572633	8
1571897	47156911	8	~1982
1571957	9431743	7	~1981
1572091	176074193	9	~1984
1572149	12577193	8	~1981
1572163	37731913	8	~1982
1572239	12577913	8	~1981
1572251	12578009	8	~1981
1572271	15722711	8	~1981
1572401	9434407	7	~1981
1572407	12579257	8	~1981
1572419	28303543	8	~1982
1572443	3144887	7	~1979
1572617	22016639	8	~1981
1572731	3145463	7	~1979
1572749	22018487	8	~1981

Exp.	Prime Factor	Digits	Year
1572749	50327969	8
1572799	204463871	9	~1984
1572803	3145607	7	~1979
1572871	66060583	8	~1983
1572911	3145823	7	~1979
1573021	9438127	7	~1981
1573109	37754617	8	~1982
1573133	9438799	7	~1981
1573139	3146279	7	~1979
1573151	3146303	7	~1979
1573217	9439303	7	~1981
1573283	3146567	7	~1979
1573543	25176689	8	~1982
1573547	28323847	8	~1982
1573577	12588617	8	~1981
1573577	125886161	9
1573613	47208391	8	~1982
1573717	100717889	9	~1983
1573811	3147623	7	~1979
1573823	88134089	8	~1983
1573927	15739271	8	~1981
1573973	9443839	7	~1981
1573997	12591977	8	~1981
1574057	12592457	8	~1981
1574231	3148463	7	~1979

Exp.	Prime Factor	Digits	Year
1574491	28340839	8	~1982
1574791	15747911	8	~1981
1574791	28346239	8
1574849	12598793	8	~1981
1574939	12599513	8	~1981
1575031	103952047	9	~1983
1575071	78753551	8	~1983
1575083	3150167	7	~1979
1575113	22051583	8	~1981
1575131	3150263	7	~1979
1575137	9450823	7	~1981
1575253	47257591	8	~1982
1575307	25204913	8	~1982
1575401	122881279	9	~1983
1575443	3150887	7	~1979
1575659	3151319	7	~1979
1575767	12606137	8	~1981
1575817	9454903	7	~1981
1575829	37819897	8	~1982
1575869	22062167	8	~1981
1575961	9455767	7	~1981
1576007	37824169	8	~1982
1576103	3152207	7	~1979
1576117	25217873	8	~1982
1576241	75659569	8	~1983

Exp.	Prime Factor	Digits	Year
1576357	63054281	8	~1983
1576501	9459007	7	~1981
1576649	12613193	8	~1981
1576649	47299471	8
1576703	3153407	7	~1979
1576717	9460303	7	~1981
1576717	47301511	8
1576871	3153743	7	~1979
1576871	113534713	9
1576931	3153863	7	~1979
1577021	9462127	7	~1981
1577071	25233137	8	~1982
1577137	9462823	7	~1981
1577153	97783487	8	~1983
1577201	12617609	8	~1981
1577293	9463759	7	~1981
1577341	9464047	7	~1981
1577377	75714097	8	~1983
1577507	28395127	8	~1982
1577573	50482337	8	~1982
1577579	37861897	8	~1982
1577671	15776711	8	~1981
1577689	160924279	9	~1984
1577701	25243217	8	~1982
1577759	12622073	8	~1981

5.307.017 digits

26-01-11