
theorem
  1319 is prime
proof
  now
    1319 = 2*659 + 1; hence not 2 divides 1319 by NAT_4:9;
    1319 = 3*439 + 2; hence not 3 divides 1319 by NAT_4:9;
    1319 = 5*263 + 4; hence not 5 divides 1319 by NAT_4:9;
    1319 = 7*188 + 3; hence not 7 divides 1319 by NAT_4:9;
    1319 = 11*119 + 10; hence not 11 divides 1319 by NAT_4:9;
    1319 = 13*101 + 6; hence not 13 divides 1319 by NAT_4:9;
    1319 = 17*77 + 10; hence not 17 divides 1319 by NAT_4:9;
    1319 = 19*69 + 8; hence not 19 divides 1319 by NAT_4:9;
    1319 = 23*57 + 8; hence not 23 divides 1319 by NAT_4:9;
    1319 = 29*45 + 14; hence not 29 divides 1319 by NAT_4:9;
    1319 = 31*42 + 17; hence not 31 divides 1319 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1319 & n is prime
  holds not n divides 1319 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
