Number Theoretic Functions
The Wolfram Language contains the world's largest collection of number theoretic functions, many based on specially developed algorithms.
Primes and Their Distribution »
Prime — the nth prime
PrimeQ — test for primality
NextPrime ▪ PrimePi ▪ PrimeOmega ▪ LogIntegral ▪ Zeta ▪ ZetaZero ▪ ...
Integer Factorization »
FactorInteger — find the factors of an integer
SquareFreeQ ▪ PrimePowerQ ▪ ...
Divisibility
GCD ▪ LCM ▪ Divisible ▪ CoprimeQ ▪ ExtendedGCD ▪ ModularInverse
EulerPhi ▪ MoebiusMu ▪ JacobiSymbol ▪ KroneckerSymbol
Congruences
Mod ▪ PowerMod ▪ MultiplicativeOrder ▪ PrimitiveRoot ▪ PrimitiveRootList ▪ ChineseRemainder ▪ PowerModList ▪ CarmichaelLambda
Divisors »
Divisors ▪ DivisorSigma ▪ DivisorSum ▪ DedekindEta ▪ EllipticTheta ▪ ...
Partitions »
IntegerPartitions ▪ PartitionsP ▪ StirlingS1 ▪ StirlingS2 ▪ FrobeniusNumber ▪ ...
Representations as Sums of Powers
SquaresR ▪ PowersRepresentations ▪ EllipticTheta
Digit Representations »
IntegerDigits ▪ NumberDigit ▪ FromDigits ▪ DigitCount ▪ IntegerReverse ▪ IntegerExponent ▪ Log2 ▪ ...
Multiplicative Number Theory »
MoebiusMu ▪ EulerPhi ▪ DivisorSigma ▪ MangoldtLambda ▪ PrimeNu ▪ ...
Analytic Number Theory »
Zeta ▪ ZetaZero ▪ RiemannSiegelZ ▪ LerchPhi ▪ DirichletL ▪ RamanujanTau ▪ ...
Additive Number Theory »
PartitionsP ▪ PartitionsQ ▪ BellB ▪ SquaresR ▪ ...
Algebraic Number Theory »
AlgebraicNumberNorm ▪ NumberFieldDiscriminant ▪ ...