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The largest known prime numbers are Mersenne primes, the largest of these known as of September 2013 bing 2^(57885161)-1, which has a whopping 17425170 decimal digits. As of ...

Erdős proved that there exist at least one prime of the form 4k+1 and at least one prime of the form 4k+3 between n and 2n for all n>6.

The hexacode graph is the incidence graph of the unique symmetric transversal design STD_2[6;3]. It is also a bipartite (0,2)-graph. The hexacode graph is a ...

5((x^5)_infty^5)/((x)_infty^6)=sum_(m=0)^inftyP(5m+4)x^m, where (x)_infty is a q-Pochhammer symbol and P(n) is the partition function P.

The nth root of the denominator B_n of the nth convergent A_n/B_n of a number x tends to a constant lim_(n->infty)B_n^(1/n) = e^beta (1) = e^(pi^2/(12ln2)) (2) = 3.275823... ...

The negabinary representation of a number n is its representation in base -2 (i.e., base negative 2). It is therefore given by the coefficients a_na_(n-1)...a_1a_0 in n = ...

pi may be computed using a number of iterative algorithms. The best known such algorithms are the Archimedes algorithm, which was derived by Pfaff in 1800, and the ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...

The Lucas numbers are the sequence of integers {L_n}_(n=1)^infty defined by the linear recurrence equation L_n=L_(n-1)+L_(n-2) (1) with L_1=1 and L_2=3. The nth Lucas number ...