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Checkout https://github.com/tczajka/ibig-rs — it’s a pure Rust crate which builds on stable, and is pretty fast.
tczajka made a benchmark of the different bigint implementations.
rug and rust-gmp were significantly faster than everything else, which also mirrors my experiences.
NOTE:
The number of mentions on this list indicates mentions on common posts plus user suggested alternatives.
Hence, a higher number means a more popular project.