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A Poulet number is a Fermat pseudoprime to base 2, denoted psp(2), i.e., a composite number n such that 2^(n-1)=1 (mod n). The first few Poulet numbers are 341, 561, 645, ...

Define a power difference prime as a number of the form n^n-(n-1)^(n-1) that is prime. The first few power difference primes then have n=2, 3, 4, 7, 11, 17, 106, 120, 1907, ...

A power floor prime sequence is a sequence of prime numbers {|_theta^n_|}_n, where |_x_| is the floor function and theta>1 is real number. It is unknown if, though extremely ...

k+2 is prime iff the 14 Diophantine equations in 26 variables wz+h+j-q=0 (1) (gk+2g+k+1)(h+j)+h-z=0 (2) 16(k+1)^3(k+2)(n+1)^2+1-f^2=0 (3) 2n+p+q+z-e=0 (4) ...

Following Ramanujan (1913-1914), write product_(k=1,3,5,...)^infty(1+e^(-kpisqrt(n)))=2^(1/4)e^(-pisqrt(n)/24)G_n (1) ...

A prime which does not divide the class number h(p) of the cyclotomic field obtained by adjoining a primitive pth root of unity to the field of rationals. A prime p is ...

Let a discrete distribution have probability function p_k, and let a second discrete distribution have probability function q_k. Then the relative entropy of p with respect ...

The residue classes of a function f(x) mod n are all possible values of the residue f(x) (mod n). For example, the residue classes of x^2 (mod 6) are {0,1,3,4}, since 0^2=0 ...

The ring of integers is the set of integers ..., -2, -1, 0, 1, 2, ..., which form a ring. This ring is commonly denoted Z (doublestruck Z), or sometimes I (doublestruck I). ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...