Small Mersenne Prime Factors (page 859/5025)

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
7472123	14944247	8	~1985
7472293	44833759	8	~1986
7472321	597785681	9	~1989
7472513	179340313	9	~1987
7472603	14945207	8	~1985
7472903	14945807	8	~1985
7472951	313863943	9	~1988
7473017	44838103	8	~1986
7473233	104625263	9	~1987
7473259	74732591	8	~1986
7473299	14946599	8	~1985
7473359	14946719	8	~1985
7473491	14946983	8	~1985
7473839	14947679	8	~1985
7474301	44845807	8	~1986
7474367	59794937	8	~1986
7474673	44848039	8	~1986
7474799	59798393	8	~1986
7474801	44848807	8	~1986
7474979	14949959	8	~1985
7475129	897015481	9	~1989
7475317	44851903	8	~1986
7475543	14951087	8	~1985
7476017	59808137	8	~1986
7476043	74760431	8	~1986

Exp.	Prime Factor	Digits	Year
7476071	14952143	8	~1985
7476263	14952527	8	~1985
7476383	14952767	8	~1985
7476433	44858599	8	~1986
7476641	44859847	8	~1986
7476743	14953487	8	~1985
7476773	44860639	8	~1986
7476779	14953559	8	~1985
7476803	14953607	8	~1985
7476851	314027743	9	~1988
7476877	44861263	8	~1986
7476961	44861767	8	~1986
7477031	14954063	8	~1985
7477031	59816249	8
7477181	59817449	8	~1986
7477361	44864167	8	~1986
7477643	14955287	8	~1985
7477919	14955839	8	~1985
7478257	44869543	8	~1986
7478363	14956727	8	~1985
7478423	14956847	8	~1985
7478573	224357191	9	~1988
7478621	44871727	8	~1986
7478831	59830649	8	~1986
7479259	74792591	8	~1986

Exp.	Prime Factor	Digits	Year
7479431	14958863	8	~1985
7479539	14959079	8	~1985
7479601	44877607	8	~1986
7479911	59839289	8	~1986
7479971	14959943	8	~1985
7480181	59841449	8	~1986
7480223	14960447	8	~1985
7480283	14960567	8	~1985
7480301	44881807	8	~1986
7480457	44882743	8	~1986
7480513	164571287	9	~1987
7480591	74805911	8	~1986
7480721	59845769	8	~1986
7481531	14963063	8	~1985
7481701	44890207	8	~1986
7481723	14963447	8	~1985
7481987	59855897	8	~1986
7482119	14964239	8	~1985
7482179	14964359	8	~1985
7482239	59857913	8	~1986
7482263	14964527	8	~1985
7482313	44893879	8	~1986
7482539	14965079	8	~1985
7482733	44896399	8	~1986
7482791	14965583	8	~1985

Exp.	Prime Factor	Digits	Year
7482829	164622239	9	~1987
7482857	44897143	8	~1986
7483019	59864153	8	~1986
7483271	14966543	8	~1985
7483403	14966807	8	~1985
7483649	59869193	8	~1986
7483733	4595012063	10	~1991
7483867	134709607	9	~1987
7483919	59871353	8	~1986
7484357	179624569	9	~1987
7484579	59876633	8	~1986
7484723	14969447	8	~1985
7485077	59880617	8	~1986
7485337	179648089	9	~1987
7485497	59883977	8	~1986
7485851	14971703	8	~1985
7486463	14972927	8	~1985
7486537	44919223	8	~1986
7486541	44919247	8	~1986
7486571	14973143	8	~1985
7486631	14973263	8	~1985
7486907	59895257	8	~1986
7487131	74871311	8	~1986
7487287	74872871	8	~1986
7487321	59898569	8	~1986

4.724.182 digits

25-04-13