In Curve25519 we typically have this generator point or base point:
Gx = 9 Gy = 14781619447589544791020593568409986887264606134616475288964881837755586237401 or: Gy' = p - Gy = 43114425171068552920764898935933967039370386198203806730763910166200978582548
p = 2^255-19, the dimension of the prime field Fp in which we evaluate the curve.
What is the order of this generator point?
i.e. what is the smallest n so nG = 0.
Before actually thinking about it, I just assumed that would be
p is prime. But obviously that's wrong as we're dealing with elliptic curve point addition here, not just scalar multiplication in modular arithmic.
So I'm wondering what is G's order, and perhaps more difficult: how can I find this myself? (once I have the value I can easily verify it, that's much less complicated)