
theorem
  1609 is prime
proof
  now
    1609 = 2*804 + 1; hence not 2 divides 1609 by NAT_4:9;
    1609 = 3*536 + 1; hence not 3 divides 1609 by NAT_4:9;
    1609 = 5*321 + 4; hence not 5 divides 1609 by NAT_4:9;
    1609 = 7*229 + 6; hence not 7 divides 1609 by NAT_4:9;
    1609 = 11*146 + 3; hence not 11 divides 1609 by NAT_4:9;
    1609 = 13*123 + 10; hence not 13 divides 1609 by NAT_4:9;
    1609 = 17*94 + 11; hence not 17 divides 1609 by NAT_4:9;
    1609 = 19*84 + 13; hence not 19 divides 1609 by NAT_4:9;
    1609 = 23*69 + 22; hence not 23 divides 1609 by NAT_4:9;
    1609 = 29*55 + 14; hence not 29 divides 1609 by NAT_4:9;
    1609 = 31*51 + 28; hence not 31 divides 1609 by NAT_4:9;
    1609 = 37*43 + 18; hence not 37 divides 1609 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1609 & n is prime
  holds not n divides 1609 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
