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{{r|Prime number}}

...states that every positive whole number can be expressed as a product of [[prime number]]s in essentially only one way. For instance, <math>12=2 \times 2 \times 3

If the natural number <math>\scriptstyle p\ </math> is a [[prime number]] then it holds that ...divides <math>\scriptstyle V_m(P,Q)-P\ </math> then is <math>m\ </math> a prime number) are individually false and lead to [[Fibonacci pseudoprime|Fibonacci pseud

...' in [[analytic number theory]] is an upper bound on the distribution on [[prime number|prime]]s in an [[arithmetic progression]]. It states that, if <math>\pi(x;

{{r|Prime number}}

...Carmichael numbers may be extended<ref>Paulo Ribenboim, ''The new book of prime number records'', Springer-Verlag (1996) ISBN 0-387-94457-5. P.120</ref> to

{{r|Prime number}}

If ''p'' is a [[prime number]] then ''p'' divides <math>\tbinom{p}{k}</math> for every <math>1<k<p\ </ma

{{r|prime number}}

{{r|Prime number}}

The '''''p''''' '''-adic''' metric, with respect to a given [[prime number]] ''p'', on the field '''Q''' of [[rational number]]s is a [[metric space|m

...ses prime factorizations. Consider the factorizations of 63 and 77 into [[prime number]]s:

For a nonnegative integer ''n'' and a prime number ''p'', the exponent <math> e_{p} </math> in the factorization is called the

...y set {0,1,...,p-1} under addition and multiplication modulo p, for any [[prime number]] p, is a field. ...eld is taken to be 0. If the characteristic of a field is nonzero, it is a prime number because otherwise, the number <math>1+1+\cdots+1</math>, where the number o

...sidered as acting on [[commutativity|commutative]] algebras or fields of [[prime number|prime]] [[characteristic of a field|characteristic]] ''p''.

* The [[Prime Number Theorem]] is equivalent to the statement that the [[von Mangoldt function]]

{{r|Prime Number Theorem}}

...used in the study of [[arithmetic function]]s and yields a proof of the [[Prime number theorem]]. It is an example of a [[Tauberian theorem]]. ...are values of the [[von Mangoldt function]], it is possible to deduce the prime number theorem from the fact that the zeta function has no zeroes on the line <mat

{{r|Prime number}}

...orm a full rectangle more than one square wide with 11 squares, so 11 is a prime number.]] ...and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, and 17. A prime number <math>p</math> cannot be factored as the [[multiplication|product]] of two