Frobenius Number Benchmark Dataset for Primitive Integer Vectors

This dataset contains 25,000 randomly generated primitive integer vectors together with exact Frobenius numbers and associated arithmetic metadata.

For a primitive integer vector a = (a1, ..., an), the Frobenius number is the largest integer that cannot be expressed as a nonnegative integer combination of the entries of a.

The dataset is intended as a benchmark resource for computational experiments on the Frobenius problem, additive number theory, optimisation, and machine learning for mathematics. It may be useful for algorithm benchmarking, experimental mathematics, and teaching in discrete mathematics, number theory, and Operations Research.

The instance families are generated from the parameter sets

• n = 2, 3, 5, 10, 20, 50, 100, 200, 500, 1000, and 
• M = 100, 1000, 10 000

where n denotes the dimension of the integer vector, and M denotes the upper bound on the vector entries. The release contains all valid parameter pairs with n<M, producing 25 benchmark instance families. Each instance family contains 1,000 randomly generated instances.

Each dataset row includes:

• the primitive integer vector,
• exact Frobenius number,
• pairwise coprimality information,
• number of coprime pairs,
• smallest coprime subvector size, and
• additional arithmetic metadata.

The release consists of CSV benchmark files, a self-contained R script used to generate the instances, and accompanying documentation provided in a Markdown file.