
theorem
  1321 is prime
proof
  now
    1321 = 2*660 + 1; hence not 2 divides 1321 by NAT_4:9;
    1321 = 3*440 + 1; hence not 3 divides 1321 by NAT_4:9;
    1321 = 5*264 + 1; hence not 5 divides 1321 by NAT_4:9;
    1321 = 7*188 + 5; hence not 7 divides 1321 by NAT_4:9;
    1321 = 11*120 + 1; hence not 11 divides 1321 by NAT_4:9;
    1321 = 13*101 + 8; hence not 13 divides 1321 by NAT_4:9;
    1321 = 17*77 + 12; hence not 17 divides 1321 by NAT_4:9;
    1321 = 19*69 + 10; hence not 19 divides 1321 by NAT_4:9;
    1321 = 23*57 + 10; hence not 23 divides 1321 by NAT_4:9;
    1321 = 29*45 + 16; hence not 29 divides 1321 by NAT_4:9;
    1321 = 31*42 + 19; hence not 31 divides 1321 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1321 & n is prime
  holds not n divides 1321 by XPRIMET1:22;
  hence thesis by NAT_4:14;
