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A short set of data that proves the primality of a number. A certificate can, in general, be checked much more quickly than the time required to generate the certificate. ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

The Euler-Maclaurin integration and sums formulas can be derived from Darboux's formula by substituting the Bernoulli polynomial B_n(t) in for the function phi(t). ...

The Glaisher-Kinkelin constant A is defined by lim_(n->infty)(H(n))/(n^(n^2/2+n/2+1/12)e^(-n^2/4))=A (1) (Glaisher 1878, 1894, Voros 1987), where H(n) is the hyperfactorial, ...

An NSW number (named after Newman, Shanks, and Williams) is an integer m that solves the Diophantine equation 2n^2=m^2+1. (1) In other words, the NSW numbers m index the ...

An algorithm for making tables of primes. Sequentially write down the integers from 2 to the highest number n you wish to include in the table. Cross out all numbers >2 which ...

An unordered factorization is a factorization of a number into a product of factors where order is ignored. The following table lists the unordered factorizations of the ...

Let n be a positive nonsquare integer. Then Artin conjectured that the set S(n) of all primes for which n is a primitive root is infinite. Under the assumption of the ...

Let the difference of successive primes be defined by d_n=p_(n+1)-p_n, and d_n^k by d_n^k={d_n for k=1; |d_(n+1)^(k-1)-d_n^(k-1)| for k>1. (1) N. L. Gilbreath claimed that ...

An integer j(n) is called a jumping champion if j(n) is the most frequently occurring difference between consecutive primes <=n (Odlyzko et al. 1999). This term was coined by ...