mod 7: division always works · mod 12: 4×3=0 · prime modulus = field · runs locally
ℤ/pℤ for prime p is a field: every nonzero element has a multiplicative inverse · ℤ/12ℤ is not: gcd(4,12)=4≠1 so 4 has no inverse · primes make fields because they're coprime to everything nonzero