
theorem
  1201 is prime
proof
  now
    1201 = 2*600 + 1; hence not 2 divides 1201 by NAT_4:9;
    1201 = 3*400 + 1; hence not 3 divides 1201 by NAT_4:9;
    1201 = 5*240 + 1; hence not 5 divides 1201 by NAT_4:9;
    1201 = 7*171 + 4; hence not 7 divides 1201 by NAT_4:9;
    1201 = 11*109 + 2; hence not 11 divides 1201 by NAT_4:9;
    1201 = 13*92 + 5; hence not 13 divides 1201 by NAT_4:9;
    1201 = 17*70 + 11; hence not 17 divides 1201 by NAT_4:9;
    1201 = 19*63 + 4; hence not 19 divides 1201 by NAT_4:9;
    1201 = 23*52 + 5; hence not 23 divides 1201 by NAT_4:9;
    1201 = 29*41 + 12; hence not 29 divides 1201 by NAT_4:9;
    1201 = 31*38 + 23; hence not 31 divides 1201 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1201 & n is prime
  holds not n divides 1201 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
