
theorem
  1559 is prime
proof
  now
    1559 = 2*779 + 1; hence not 2 divides 1559 by NAT_4:9;
    1559 = 3*519 + 2; hence not 3 divides 1559 by NAT_4:9;
    1559 = 5*311 + 4; hence not 5 divides 1559 by NAT_4:9;
    1559 = 7*222 + 5; hence not 7 divides 1559 by NAT_4:9;
    1559 = 11*141 + 8; hence not 11 divides 1559 by NAT_4:9;
    1559 = 13*119 + 12; hence not 13 divides 1559 by NAT_4:9;
    1559 = 17*91 + 12; hence not 17 divides 1559 by NAT_4:9;
    1559 = 19*82 + 1; hence not 19 divides 1559 by NAT_4:9;
    1559 = 23*67 + 18; hence not 23 divides 1559 by NAT_4:9;
    1559 = 29*53 + 22; hence not 29 divides 1559 by NAT_4:9;
    1559 = 31*50 + 9; hence not 31 divides 1559 by NAT_4:9;
    1559 = 37*42 + 5; hence not 37 divides 1559 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1559 & n is prime
  holds not n divides 1559 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
