
theorem
  421 is prime
proof
  now
    421 = 2*210 + 1; hence not 2 divides 421 by NAT_4:9;
    421 = 3*140 + 1; hence not 3 divides 421 by NAT_4:9;
    421 = 5*84 + 1; hence not 5 divides 421 by NAT_4:9;
    421 = 7*60 + 1; hence not 7 divides 421 by NAT_4:9;
    421 = 11*38 + 3; hence not 11 divides 421 by NAT_4:9;
    421 = 13*32 + 5; hence not 13 divides 421 by NAT_4:9;
    421 = 17*24 + 13; hence not 17 divides 421 by NAT_4:9;
    421 = 19*22 + 3; hence not 19 divides 421 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 421 & n is prime
  holds not n divides 421 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
