
theorem
  1453 is prime
proof
  now
    1453 = 2*726 + 1; hence not 2 divides 1453 by NAT_4:9;
    1453 = 3*484 + 1; hence not 3 divides 1453 by NAT_4:9;
    1453 = 5*290 + 3; hence not 5 divides 1453 by NAT_4:9;
    1453 = 7*207 + 4; hence not 7 divides 1453 by NAT_4:9;
    1453 = 11*132 + 1; hence not 11 divides 1453 by NAT_4:9;
    1453 = 13*111 + 10; hence not 13 divides 1453 by NAT_4:9;
    1453 = 17*85 + 8; hence not 17 divides 1453 by NAT_4:9;
    1453 = 19*76 + 9; hence not 19 divides 1453 by NAT_4:9;
    1453 = 23*63 + 4; hence not 23 divides 1453 by NAT_4:9;
    1453 = 29*50 + 3; hence not 29 divides 1453 by NAT_4:9;
    1453 = 31*46 + 27; hence not 31 divides 1453 by NAT_4:9;
    1453 = 37*39 + 10; hence not 37 divides 1453 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1453 & n is prime
  holds not n divides 1453 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
