
theorem
  1399 is prime
proof
  now
    1399 = 2*699 + 1; hence not 2 divides 1399 by NAT_4:9;
    1399 = 3*466 + 1; hence not 3 divides 1399 by NAT_4:9;
    1399 = 5*279 + 4; hence not 5 divides 1399 by NAT_4:9;
    1399 = 7*199 + 6; hence not 7 divides 1399 by NAT_4:9;
    1399 = 11*127 + 2; hence not 11 divides 1399 by NAT_4:9;
    1399 = 13*107 + 8; hence not 13 divides 1399 by NAT_4:9;
    1399 = 17*82 + 5; hence not 17 divides 1399 by NAT_4:9;
    1399 = 19*73 + 12; hence not 19 divides 1399 by NAT_4:9;
    1399 = 23*60 + 19; hence not 23 divides 1399 by NAT_4:9;
    1399 = 29*48 + 7; hence not 29 divides 1399 by NAT_4:9;
    1399 = 31*45 + 4; hence not 31 divides 1399 by NAT_4:9;
    1399 = 37*37 + 30; hence not 37 divides 1399 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1399 & n is prime
  holds not n divides 1399 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
