Month: December 2025
Implementation of the Randomized Cubic Primality Test in Python
This post provides a complete, runnable Python implementation of the randomized cubic primality test using explicit Frobenius computation in a cubic ring, as described in my article “A Randomized Cubic Primality Test Using Explicit Frobenius Computation”. The test operates in the ring $$R_N = (\mathbb{Z}/N\mathbb{Z})[x]/(f(x)),\qquad f(x)=x^3-qx-q,$$ where $N$ is the integer under test and $q$… Continue reading Implementation of the Randomized Cubic Primality Test in Python
A Randomized Cubic Primality Test Using Explicit Frobenius Computation
A Cubic Primality Test Based on Explicit Frobenius Computation. According to this document from July 10, 2025, the core idea is to build a primality test by explicitly computing the Frobenius action in a cubic extension and comparing it to a predicted conjugate. The randomized version below keeps the same mathematics, but replaces “search for… Continue reading A Randomized Cubic Primality Test Using Explicit Frobenius Computation