
theorem
  1459 is prime
proof
  now
    1459 = 2*729 + 1; hence not 2 divides 1459 by NAT_4:9;
    1459 = 3*486 + 1; hence not 3 divides 1459 by NAT_4:9;
    1459 = 5*291 + 4; hence not 5 divides 1459 by NAT_4:9;
    1459 = 7*208 + 3; hence not 7 divides 1459 by NAT_4:9;
    1459 = 11*132 + 7; hence not 11 divides 1459 by NAT_4:9;
    1459 = 13*112 + 3; hence not 13 divides 1459 by NAT_4:9;
    1459 = 17*85 + 14; hence not 17 divides 1459 by NAT_4:9;
    1459 = 19*76 + 15; hence not 19 divides 1459 by NAT_4:9;
    1459 = 23*63 + 10; hence not 23 divides 1459 by NAT_4:9;
    1459 = 29*50 + 9; hence not 29 divides 1459 by NAT_4:9;
    1459 = 31*47 + 2; hence not 31 divides 1459 by NAT_4:9;
    1459 = 37*39 + 16; hence not 37 divides 1459 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1459 & n is prime
  holds not n divides 1459 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
