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A gigantic prime is a prime with 10000 or more decimal digits. The first few gigantic primes are given by 10^(9999)+n for n=33603, 55377, 70999, 78571, 97779, 131673, 139579, ...

The square-triangle theorem states that any nonnegative integer can be represented as the sum of a square, an even square, and a triangular number (Sun 2005), i.e., ...

A prime factor is a factor that is prime, i.e., one that cannot itself be factored. In general, a prime factorization takes the form ...

Let T(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Define f_m(x)=product_(t in T(m))(x-t). (1) Then a ...

A Størmer number is a positive integer n for which the greatest prime factor p of n^2+1 is at least 2n. Every Gregory number t_x can be expressed uniquely as a sum of t_ns ...

The Fermat number F_n is prime iff 3^(2^(2^n-1))=-1 (mod F_n).

A square-free graph is a graph containing no graph cycles of length four. A simple graph is square-free iff c_4=1/8[Tr(A^4)-2m-2sum_(i!=j)a_(ij)^((2))]=0, where A is the ...

The graph complement of a graph hole. Graph antiholes are called even if they have an even number of vertices and odd if they have an odd number of vertices (Chvátal). No odd ...

Let a!=b, A, and B denote positive integers satisfying (a,b)=1 (A,B)=1, (i.e., both pairs are relatively prime), and suppose every prime p=B (mod A) with (p,2ab)=1 is ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...