how is the order determined for Secp256k1?

[graphite]

I haven't been able to find any resource that explains how the order of Spec256k1 is found or for any other elliptic curve cryptography functions. The only hint Ive read is that the order (n) is usually somewhere near the prime field (p)

   p = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F
   n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141

the order and price field are around 2^128 away from each other. This means if you were to brute force search for n using the p as a starting point it would take 2^64 iterations to hit n. Did they brute force n or is there a simpler solution to this?

[gmaxwell]

is that the order (n) is usually somewhere near the prime field (p)

https://en.wikipedia.org/wiki/Hasse%27s_theorem_on_elliptic_curves

Did they brute force n or is there a simpler solution to this?

https://en.wikipedia.org/wiki/Counting_points_on_elliptic_curves#Schoof%E2%80%93Elkies%E2%80%93Atkin_algorithm