Small Mersenne Prime Factors (page 878/5610)

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
7283833	43702999	8	~1986
7283891	14567783	8	~1985
7283999	14567999	8	~1985
7284131	14568263	8	~1985
7284197	43705183	8	~1986
7284443	14568887	8	~1985
7284493	43706959	8	~1986
7284749	174833977	9	~1987
7284971	14569943	8	~1985
7285049	101990687	9	~1987
7285081	43710487	8	~1986
7285219	131133943	9	~1987
7285391	4210955999	10	~1991
7285919	58287353	8	~1986
7286099	14572199	8	~1985
7286137	291445481	9	~1988
7286311	116580977	9	~1987
7286687	58293497	8	~1986
7286803	72868031	8	~1986
7287097	43722583	8	~1986
7287359	14574719	8	~1985
7287437	43724623	8	~1986
7287571	72875711	8	~1986
7287851	131181319	9	~1987
7287911	14575823	8	~1985

Exp.	Prime Factor	Digits	Year
7288103	14576207	8	~1985
7288159	72881591	8	~1986
7288163	174915913	9	~1987
7288181	43729087	8	~1986
7288273	43729639	8	~1986
7288399	72883991	8	~1986
7288691	14577383	8	~1985
7288763	14577527	8	~1985
7288843	116621489	9	~1987
7289099	14578199	8	~1985
7289279	14578559	8	~1985
7289339	14578679	8	~1985
7289363	14578727	8	~1985
7289519	14579039	8	~1985
7289599	1530815791	10	~1990
7289669	58317353	8	~1986
7290191	14580383	8	~1985
7290359	14580719	8	~1985
7290541	43743247	8	~1986
7290557	58324457	8	~1986
7290863	14581727	8	~1985
7290971	58327769	8	~1986
7291121	58328969	8	~1986
7291607	131248927	9	~1987
7291819	72918191	8	~1986

Exp.	Prime Factor	Digits	Year
7291831	306256903	9	~1988
7292063	14584127	8	~1985
7292083	72920831	8	~1986
7292237	1152173447	10	~1989
7292381	43754287	8	~1986
7292381	58339049	8
7292401	160432823	9	~1987
7292501	43755007	8	~1986
7292693	102097703	9	~1987
7292707	247952039	9	~1988
7292819	14585639	8	~1985
7292821	43756927	8	~1986
7292851	131271319	9	~1987
7293371	14586743	8	~1985
7293431	14586863	8	~1985
7293487	72934871	8	~1986
7293497	58347977	8	~1986
7293719	14587439	8	~1985
7293899	14587799	8	~1985
7293911	14587823	8	~1985
7294201	43765207	8	~1986
7294409	58355273	8	~1986
7294571	58356569	8	~1986
7294757	58358057	8	~1986
7295003	14590007	8	~1985

Exp.	Prime Factor	Digits	Year
7295201	43771207	8	~1986
7295231	14590463	8	~1985
7295471	14590943	8	~1985
7295471	58363769	8
7295699	14591399	8	~1985
7295719	72957191	8	~1986
7295759	58366073	8	~1986
7295863	72958631	8	~1986
7296127	72961271	8	~1986
7296379	72963791	8	~1986
7296427	72964271	8	~1986
7296781	43780687	8	~1986
7296841	335654687	9	~1988
7296851	14593703	8	~1985
7296973	43781839	8	~1986
7297127	58377017	8	~1986
7297271	58378169	8	~1986
7297379	58379033	8	~1986
7297571	14595143	8	~1985
7297711	116763377	9	~1987
7297933	43787599	8	~1986
7298177	58385417	8	~1986
7298231	58385849	8	~1986
7298591	14597183	8	~1985
7298663	14597327	8	~1985

5.307.017 digits

26-01-11