Number Theoretic Functions

The Wolfram Language contains the world's largest collection of number theoretic functions, many based on specially developed algorithms.

(OrangeLink[Primes and Their Distribution », paclet:guide/PrimeNumbers])

(RefLink[Prime, paclet:ref/Prime]) — the n(^th) prime

(RefLink[PrimeQ, paclet:ref/PrimeQ]) — test for primality

(OrangeLink[Integer Factorization », paclet:guide/PrimeNumbers])

(RefLink[FactorInteger, paclet:ref/FactorInteger]) — find the factors of an integer

Divisibility

Congruences

(OrangeLink[Divisors », paclet:guide/MultiplicativeNumberTheory])

(OrangeLink[Partitions », paclet:guide/AdditiveNumberTheory])

Representations as Sums of Powers

(OrangeLink[Digit Representations », paclet:guide/NumberDigits])

(OrangeLink[Multiplicative Number Theory », paclet:guide/MultiplicativeNumberTheory])

(OrangeLink[Analytic Number Theory », paclet:guide/AnalyticNumberTheory])

(OrangeLink[Additive Number Theory », paclet:guide/AdditiveNumberTheory])

(OrangeLink[Algebraic Number Theory », paclet:guide/AlgebraicNumberTheory])