flâneur

Math & Engineering

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Random collections of my notes and articles over the years, mostly about maths and/or engineering.

The Goldilocks Prime \gdef\delim#1#2#3{\mathopen{}\mathclose{\left#1 #2 \right#3}} \gdef\F{\mathbb{F}} \gdef\mod#1{\delim[{#1}]} In Ham15 Mike Hamburg introduced a class of primes of the form p = φ^2 - φ - 1 and named them Goldilocks primes. In those prime fields φ satisfies the Golden ratio relation φ² = φ + 1 . When φ is a power of two this allows for very efficient implementation. Unfortunately, the -1 at the end means it will have very few power-of-two roots of unity. We'd like to have many so we can do big number theoretic transforms. We will instead consider primes of the form p = φ^2 -

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