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Built-in Mathematica Symbol

CoprimeQ

CoprimeQ[n₁, n₂]
yields True if n₁ and n₂ are relatively prime, and yields False otherwise.

CoprimeQ[n₁, n₂, ...]
yields True if all pairs of the n_i are relatively prime, and yields False otherwise.

8, 9 and 11 are relatively prime:

CoprimeQ works with numbers of any size:

CoprimeQ threads itself element-wise over lists:

Gaussian integers:

Plot pairs of numbers that are relatively prime:

Find the fraction of pairs of the first 100 numbers that are relatively prime:

The result is close to

Find the first 2x2 block of white squares in the array of coprime numbers:

Plot which triples of numbers are relatively prime:

2D slices: