WaitNext[{eid_1, eid_2, ...}] waits until the first evaluation represented by any of the eid_i finishes, then returns its result, the corresponding eid_i, and the list of ...

Mathematica's extensive base of state-of-the-art algorithms, efficient handling of very long integers, and powerful built-in language make it uniquely suited to both research ...

MoebiusMu[n] gives the Möbius function \[Mu](n).

With its convenient symbolic representation of algebraic numbers, Mathematica's state-of-the-art algebraic number theory capabilities provide a concrete implementation of one ...

Mathematica contains hundreds of original algorithms for computing integer functions involving integers of any size.

The primes have been a focal point for investigations of numbers for more than two millennia. Mathematica implements state-of-the-art algorithms for handling both primes and ...

LiouvilleLambda[n] gives the Liouville function \[Lambda](n).

MangoldtLambda[n] gives the von Mangoldt function \[CapitalLambda](n).

SquareFreeQ[expr] gives True if expr is a square-free polynomial or number, and False otherwise.SquareFreeQ[expr, vars] gives True if expr is square free with respect to the ...

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