Used gmpy2 functions instead of the standard ones or the while-loops implemented in Python #2
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The gmpy2 functions are from 50% to up to 400% faster. You can run your own benchmarks or run https://github.com/maximmasiutin/rsa-common-modulus/blob/main/test/benchmark-libs.py to find the real difference on your computer. I've run my tests on a notebook with Intel Core i7 1065G7 (AVX-512), gmpy2 version: 2.1.0b3, Python version: 3.8.5.
The most significant difference is between the gmpy2 invert(a, b) and Python's pow(a, -1, b).