
theorem
  1699 is prime
proof
  now
    1699 = 2*849 + 1; hence not 2 divides 1699 by NAT_4:9;
    1699 = 3*566 + 1; hence not 3 divides 1699 by NAT_4:9;
    1699 = 5*339 + 4; hence not 5 divides 1699 by NAT_4:9;
    1699 = 7*242 + 5; hence not 7 divides 1699 by NAT_4:9;
    1699 = 11*154 + 5; hence not 11 divides 1699 by NAT_4:9;
    1699 = 13*130 + 9; hence not 13 divides 1699 by NAT_4:9;
    1699 = 17*99 + 16; hence not 17 divides 1699 by NAT_4:9;
    1699 = 19*89 + 8; hence not 19 divides 1699 by NAT_4:9;
    1699 = 23*73 + 20; hence not 23 divides 1699 by NAT_4:9;
    1699 = 29*58 + 17; hence not 29 divides 1699 by NAT_4:9;
    1699 = 31*54 + 25; hence not 31 divides 1699 by NAT_4:9;
    1699 = 37*45 + 34; hence not 37 divides 1699 by NAT_4:9;
    1699 = 41*41 + 18; hence not 41 divides 1699 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1699 & n is prime
  holds not n divides 1699 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
