
theorem
  1601 is prime
proof
  now
    1601 = 2*800 + 1; hence not 2 divides 1601 by NAT_4:9;
    1601 = 3*533 + 2; hence not 3 divides 1601 by NAT_4:9;
    1601 = 5*320 + 1; hence not 5 divides 1601 by NAT_4:9;
    1601 = 7*228 + 5; hence not 7 divides 1601 by NAT_4:9;
    1601 = 11*145 + 6; hence not 11 divides 1601 by NAT_4:9;
    1601 = 13*123 + 2; hence not 13 divides 1601 by NAT_4:9;
    1601 = 17*94 + 3; hence not 17 divides 1601 by NAT_4:9;
    1601 = 19*84 + 5; hence not 19 divides 1601 by NAT_4:9;
    1601 = 23*69 + 14; hence not 23 divides 1601 by NAT_4:9;
    1601 = 29*55 + 6; hence not 29 divides 1601 by NAT_4:9;
    1601 = 31*51 + 20; hence not 31 divides 1601 by NAT_4:9;
    1601 = 37*43 + 10; hence not 37 divides 1601 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1601 & n is prime
  holds not n divides 1601 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
