
theorem
  997 is prime
proof
  now
    997 = 2*498 + 1; hence not 2 divides 997 by NAT_4:9;
    997 = 3*332 + 1; hence not 3 divides 997 by NAT_4:9;
    997 = 5*199 + 2; hence not 5 divides 997 by NAT_4:9;
    997 = 7*142 + 3; hence not 7 divides 997 by NAT_4:9;
    997 = 11*90 + 7; hence not 11 divides 997 by NAT_4:9;
    997 = 13*76 + 9; hence not 13 divides 997 by NAT_4:9;
    997 = 17*58 + 11; hence not 17 divides 997 by NAT_4:9;
    997 = 19*52 + 9; hence not 19 divides 997 by NAT_4:9;
    997 = 23*43 + 8; hence not 23 divides 997 by NAT_4:9;
    997 = 29*34 + 11; hence not 29 divides 997 by NAT_4:9;
    997 = 31*32 + 5; hence not 31 divides 997 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 997 & n is prime
  holds not n divides 997 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
