Understanding the Order of Secp256k1

Anyone know how they figure out the order for Secp256k1? I can't find much info on this or on other elliptic curves. I heard that the order (n) is usually close to the prime field (p). Like, p is this huge number and n is also big but kinda far from p. From what I gather, brute forcing n from p would take forever, like 2^64 tries. Seems wild, right?

It's actually more complicated than just brute forcing. There are mathematical theorems, like Hasse's theorem, that help with point counting on elliptic curves. The Schoof-Elkies-Atkin algorithm is a key method used to efficiently determine the order of the curve. So yeah, brute force isn't the way to go. Plus, the relationship between n and p isn’t just random; they’re derived from the curve’s properties. Check those links for more in-depth info if you're interested.