# Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

## Sharpening “Primes is in P” for a large family of numbersHTML articles powered by AMS MathViewer

by Pedro Berrizbeitia
Math. Comp. 74 (2005), 2043-2059 Request permission

## Abstract:

We present algorithms that are deterministic primality tests for a large family of integers, namely, integers $n \equiv 1\pmod 4$ for which an integer $a$ is given such that the Jacobi symbol $(\frac {a}{n})= -1$, and integers $n \equiv {-1} \pmod 4$ for which an integer $a$ is given such that $(\frac {a}{n})= (\frac {1-a}{n})=-1$. The algorithms we present run in $2^{-\min (k,[2 \log \log n])} \tilde {O}((\log n)^6)$ time, where $k = \nu _2(n-1)$ is the exact power of $2$ dividing $n-1$ when $n \equiv 1\pmod 4$ and $k = \nu _2(n+1)$ if $n \equiv \ -1\pmod 4$. The complexity of our algorithms improves up to $\tilde {O}((\log n)^4)$ when $k \geq [2 \log \log n]$. We also give tests for a more general family of numbers and study their complexity.
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