
theorem
  149 is prime
proof
  now
    149 = 2*74 + 1; hence not 2 divides 149 by NAT_4:9;
    149 = 3*49 + 2; hence not 3 divides 149 by NAT_4:9;
    149 = 5*29 + 4; hence not 5 divides 149 by NAT_4:9;
    149 = 7*21 + 2; hence not 7 divides 149 by NAT_4:9;
    149 = 11*13 + 6; hence not 11 divides 149 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 149 & n is prime
  holds not n divides 149 by XPRIMET1:10;
  hence thesis by NAT_4:14;
end;
