
theorem
  1009 is prime
proof
  now
    1009 = 2*504 + 1; hence not 2 divides 1009 by NAT_4:9;
    1009 = 3*336 + 1; hence not 3 divides 1009 by NAT_4:9;
    1009 = 5*201 + 4; hence not 5 divides 1009 by NAT_4:9;
    1009 = 7*144 + 1; hence not 7 divides 1009 by NAT_4:9;
    1009 = 11*91 + 8; hence not 11 divides 1009 by NAT_4:9;
    1009 = 13*77 + 8; hence not 13 divides 1009 by NAT_4:9;
    1009 = 17*59 + 6; hence not 17 divides 1009 by NAT_4:9;
    1009 = 19*53 + 2; hence not 19 divides 1009 by NAT_4:9;
    1009 = 23*43 + 20; hence not 23 divides 1009 by NAT_4:9;
    1009 = 29*34 + 23; hence not 29 divides 1009 by NAT_4:9;
    1009 = 31*32 + 17; hence not 31 divides 1009 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1009 & n is prime
  holds not n divides 1009 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
