
theorem
  1013 is prime
proof
  now
    1013 = 2*506 + 1; hence not 2 divides 1013 by NAT_4:9;
    1013 = 3*337 + 2; hence not 3 divides 1013 by NAT_4:9;
    1013 = 5*202 + 3; hence not 5 divides 1013 by NAT_4:9;
    1013 = 7*144 + 5; hence not 7 divides 1013 by NAT_4:9;
    1013 = 11*92 + 1; hence not 11 divides 1013 by NAT_4:9;
    1013 = 13*77 + 12; hence not 13 divides 1013 by NAT_4:9;
    1013 = 17*59 + 10; hence not 17 divides 1013 by NAT_4:9;
    1013 = 19*53 + 6; hence not 19 divides 1013 by NAT_4:9;
    1013 = 23*44 + 1; hence not 23 divides 1013 by NAT_4:9;
    1013 = 29*34 + 27; hence not 29 divides 1013 by NAT_4:9;
    1013 = 31*32 + 21; hence not 31 divides 1013 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1013 & n is prime
  holds not n divides 1013 by XPRIMET1:22;
  hence thesis by NAT_4:14;
