What's 2^64 - 2^32 + 1 called?

Many zero-knowledge blockchain projects use the prime 2^{64} - 2^{32} + 1 because of its properties.

Few agree on a good name for it. People call it “the Goldilocks prime”, which is evidently the wrong name, since the Goldilocks prime is 2^{448} - 2^{224} - 1 named by Mike Hamburg in the context of the Ed448-Goldilocks elliptic curve.

You could say that our favourite prime is Goldilock-ish because it almost fits the same golden ratio form ϕ²-ϕ-1 as the Goldilocks prime, but almost fitting an expression seems like a poor guideline for naming something.

Can we name it something else?

We tried naming it B after Bobbin, but he doesn’t want the credit. (Also, I think you shouldn’t name things after people who are alive without their consent.) Other suggested name is: The Oxfoi prime, since its binary representation is 0x1111…0001, and there are very few primes that look like this. (In fact, we only found one other.)

Could the ZK Podcast community make a naming competition?

For now we call it “P”. But that gets old quick.

Just for historical accuracy, the use of the Goldilocks Prime was initially proposed by our teammate at Polygon, Hamish Ivey-Law, here: Investigate other field options · Issue #1 · mir-protocol/plonky2 · GitHub

Personally, I don’t think that it’s a big deal if “Goldilocks” was used previously, and the Goldilocks name seems to have caught on.

1 Like