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The prime HP(n) reached starting from a number n, concatenating its prime factors, and repeating until a prime is reached. For example, for n=9, 9=3·3->33=3·11->311, so 311 ...

A palindromic number is a number (in some base b) that is the same when written forwards or backwards, i.e., of the form a_1a_2...a_2a_1. The first few palindromic numbers ...

A McNugget number is a positive integer that can be obtained by adding together orders of McDonald's® Chicken McNuggetsTM (prior to consuming any), which originally came in ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, .... In formal set theory, a cardinal number (also called "the ...

The Schnirelmann density of a set of nonnegative integers is the greatest lower bound of the fractions A(n)/n where A(n) is the number of terms in the set <=n.

The ratio of two numbers r and s is written r/s, where r is the numerator and s is the denominator. The ratio of r to s is equivalent to the quotient r/s. Betting odds ...

Algebraic number theory is the branch of number theory that deals with algebraic numbers. Historically, algebraic number theory developed as a set of tools for solving ...

Computational number theory is the branch of number theory concerned with finding and implementing efficient computer algorithms for solving various problems in number ...

A lucky number of Euler is a number p such that the prime-generating polynomial n^2-n+p is prime for n=1, 2, ..., p-1. Such numbers are related to the imaginary quadratic ...