Supercomputing,

You seem to be mistaken: Source
Let us summarize: in the prime case the domain parameters are (p,a,b,G,n,h) and in the binary case they are (m,f,a,b,G,n,h)

The prime field contains a prime in the domain parameters, but the binary does not. Prime based curves use p as the prime generating the security as you stated, Binary curves use m and f. Coinshield uses sect571r1 which is a NIST/SECG curve over a 571 bit binary field