PrimeOmega (Built-in Mathematica Symbol)

PrimeOmega[n] gives the number of prime factors counting multiplicities \[CapitalOmega](n) in n.

PrimeNu (Built-in Mathematica Symbol)

PrimeNu[n] gives the number of distinct primes \[Nu](n) in n.

CoprimeQ (Built-in Mathematica Symbol)

CoprimeQ[n_1, n_2] yields True if n_1 and n_2 are relatively prime, and yields False otherwise. CoprimeQ[n_1, n_2, ...] yields True if all pairs of the n_i are relatively ...

SpheroidalS1Prime (Built-in Mathematica Symbol)

SpheroidalS1Prime[n, m, \[Gamma], z] gives the derivative with respect to z of the radial spheroidal function S_n^m, (1)(\[Gamma], z) of the first kind.

SpheroidalS2Prime (Built-in Mathematica Symbol)

SpheroidalS2Prime[n, m, \[Gamma], z] gives the derivative with respect to z of the radial spheroidal function S_n^m, (2)(\[Gamma], z) of the second kind.

PrimeZetaP (Built-in Mathematica Symbol)

PrimeZetaP[s] gives prime zeta function P(s).

RiemannR (Built-in Mathematica Symbol)

RiemannR[x] gives the Riemann prime counting function R(x).

Modulus (Built-in Mathematica Symbol)

Modulus -> n is an option that can be given in certain algebraic functions to specify that integers should be treated modulo n.

Analytic Number Theory (Mathematica Guide)

Building on its broad strengths in mathematics in general, and in special functions in particular, Mathematica provides a unique level of support for analytic number theory, ...

IrreduciblePolynomialQ (Built-in Mathematica Symbol)

IrreduciblePolynomialQ[poly] tests whether poly is an irreducible polynomial over the rationals.IrreduciblePolynomialQ[poly, Modulus -> p] tests whether poly is irreducible ...