points on curve secp256k1 form a group E(Fp) over field Fp.
p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1 is prime.
n is the order of group E, n=115792089237316195423570985008687907852837564279074904382605163141518161494337
Is n prime too?
Is E(Fp) a cyclic group?
Theorem. Working over a finite field, the group of points E(Fp) is always either a cyclic group or the product of two cyclic groups.