
theorem
  191 is prime
proof
  now
    191 = 2*95 + 1; hence not 2 divides 191 by NAT_4:9;
    191 = 3*63 + 2; hence not 3 divides 191 by NAT_4:9;
    191 = 5*38 + 1; hence not 5 divides 191 by NAT_4:9;
    191 = 7*27 + 2; hence not 7 divides 191 by NAT_4:9;
    191 = 11*17 + 4; hence not 11 divides 191 by NAT_4:9;
    191 = 13*14 + 9; hence not 13 divides 191 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 191 & n is prime
  holds not n divides 191 by XPRIMET1:12;
  hence thesis by NAT_4:14;
end;
