
theorem
  1789 is prime
proof
  now
    1789 = 2*894 + 1; hence not 2 divides 1789 by NAT_4:9;
    1789 = 3*596 + 1; hence not 3 divides 1789 by NAT_4:9;
    1789 = 5*357 + 4; hence not 5 divides 1789 by NAT_4:9;
    1789 = 7*255 + 4; hence not 7 divides 1789 by NAT_4:9;
    1789 = 11*162 + 7; hence not 11 divides 1789 by NAT_4:9;
    1789 = 13*137 + 8; hence not 13 divides 1789 by NAT_4:9;
    1789 = 17*105 + 4; hence not 17 divides 1789 by NAT_4:9;
    1789 = 19*94 + 3; hence not 19 divides 1789 by NAT_4:9;
    1789 = 23*77 + 18; hence not 23 divides 1789 by NAT_4:9;
    1789 = 29*61 + 20; hence not 29 divides 1789 by NAT_4:9;
    1789 = 31*57 + 22; hence not 31 divides 1789 by NAT_4:9;
    1789 = 37*48 + 13; hence not 37 divides 1789 by NAT_4:9;
    1789 = 41*43 + 26; hence not 41 divides 1789 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1789 & n is prime
  holds not n divides 1789 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
