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Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

1. Zero is a number. 2. If a is a number, the successor of a is a number. 3. zero is not the successor of a number. 4. Two numbers of which the successors are equal are ...

A primefree sequence is sequence whose terms are never prime. Graham (1964) proved that there exist relatively prime positive integers a and b such that the recurrence ...

The sequence {|_(3/2)^n_|} is given by 1, 1, 2, 3, 5, 7, 11, 17, 25, 38, ... (OEIS A002379). The first few composite |_(3/2)^n_| occur for n=8, 9, 10, 11, 12, 13, 14, 15, 16, ...

When a number is expressed in scientific notation, the number of significant digits (or significant figures) is the number of digits needed to express the number to within ...

A number of the form a_0+a_1zeta+...+a_(p-1)zeta^(p-1), where zeta=e^(2pii/p) is a de Moivre number and p is a prime number. Unique factorizations of cyclotomic integers fail ...

When ac is divisible by a number b that is relatively prime to a, then c must be divisible by b.

If a prime number divides a norm but not the bases of the norm, it is itself a norm.

An integer n which is tested to see if it divides a given number.

The polyhedral formula generalized to a surface of genus g, V-E+F=chi(g) where V is the number of polyhedron vertices, E is the number of polyhedron edges, F is the number of ...