
theorem
  1669 is prime
proof
  now
    1669 = 2*834 + 1; hence not 2 divides 1669 by NAT_4:9;
    1669 = 3*556 + 1; hence not 3 divides 1669 by NAT_4:9;
    1669 = 5*333 + 4; hence not 5 divides 1669 by NAT_4:9;
    1669 = 7*238 + 3; hence not 7 divides 1669 by NAT_4:9;
    1669 = 11*151 + 8; hence not 11 divides 1669 by NAT_4:9;
    1669 = 13*128 + 5; hence not 13 divides 1669 by NAT_4:9;
    1669 = 17*98 + 3; hence not 17 divides 1669 by NAT_4:9;
    1669 = 19*87 + 16; hence not 19 divides 1669 by NAT_4:9;
    1669 = 23*72 + 13; hence not 23 divides 1669 by NAT_4:9;
    1669 = 29*57 + 16; hence not 29 divides 1669 by NAT_4:9;
    1669 = 31*53 + 26; hence not 31 divides 1669 by NAT_4:9;
    1669 = 37*45 + 4; hence not 37 divides 1669 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1669 & n is prime
  holds not n divides 1669 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
