Small Mersenne Prime Factors (page 366/5745)

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
1780027	17800271	8	~1982
1780253	24923543	8	~1982
1780321	28485137	8	~1982
1780379	3560759	7	~1980
1780379	56972129	8
1780381	28486097	8	~1982
1780411	32047399	8	~1982
1780447	17804471	8	~1982
1780463	3560927	7	~1980
1780517	10683103	8	~1981
1780577	14244617	8	~1981
1780663	17806631	8	~1982
1780703	3561407	7	~1980
1780901	10685407	8	~1981
1780967	32057407	8	~1982
1781027	14248217	8	~1981
1781047	28496753	8	~1982
1781099	3562199	7	~1980
1781239	42749737	8	~1982
1781287	42750889	8	~1982
1781309	24938327	8	~1982
1781363	74817247	8	~1983
1781519	3563039	7	~1980
1781609	14252873	8	~1981
1781831	32072959	8	~1982

Exp.	Prime Factor	Digits	Year
1781851	17818511	8	~1982
1781893	28510289	8	~1982
1782113	42770713	8	~1982
1782239	3564479	7	~1980
1782563	3565127	7	~1980
1782589	42782137	8	~1982
1782611	14260889	8	~1981
1782743	3565487	7	~1980
1782769	39220919	8	~1982
1782797	10696783	8	~1981
1782829	42787897	8	~1982
1782917	10697503	8	~1981
1782961	10697767	8	~1981
1783043	42793033	8	~1982
1783163	3566327	7	~1980
1783423	17834231	8	~1982
1783427	14267417	8	~1981
1783469	14267753	8	~1981
1783643	57076577	8	~1983
1783781	10702687	8	~1981
1783813	39243887	8	~1982
1783921	10703527	8	~1981
1784203	17842031	8	~1982
1784231	3568463	7	~1980
1784281	10705687	8	~1981

Exp.	Prime Factor	Digits	Year
1784389	71375561	8	~1983
1784557	10707343	8	~1981
1784633	10707799	8	~1981
1784641	28554257	8	~1982
1784647	17846471	8	~1982
1784833	71393321	8	~1983
1784963	3569927	7	~1980
1785257	24993599	8	~1982
1785347	89267351	8	~1983
1785401	85699249	8	~1983
1785419	3570839	7	~1980
1785473	24996623	8	~1982
1785491	32138839	8	~1982
1785599	3571199	7	~1980
1785613	114279233	9	~1984
1785683	589275391	9	~1985
1785713	10714279	8	~1981
1785779	3571559	7	~1980
1785779	57144929	8
1785811	28572977	8	~1982
1785961	10715767	8	~1981
1785961	28575377	8
1785977	25003679	8	~1982
1786201	39296423	8	~1982
1786223	3572447	7	~1980

Exp.	Prime Factor	Digits	Year
1786277	67878527	8	~1983
1786331	3572663	7	~1980
1786363	17863631	8	~1982
1786439	3572879	7	~1980
1786439	42874537	8
1786451	3572903	7	~1980
1786591	28585457	8	~1982
1786591	32158639	8
1786753	10720519	8	~1981
1786787	100060073	9	~1983
1786843	60752663	8	~1983
1786943	3573887	7	~1980
1787033	25018463	8	~1982
1787039	3574079	7	~1980
1787129	14297033	8	~1981
1787129	57188129	8
1787143	17871431	8	~1982
1787179	71487161	8	~1983
1787293	10723759	8	~1981
1787437	42898489	8	~1982
1787573	10725439	8	~1981
1787587	32176567	8	~1982
1787707	17877071	8	~1982
1788187	28610993	8	~1982
1788239	3576479	7	~1980

5.441.361 digits

26-03-15