
theorem
  6653 is prime
proof
  now
    6653 = 2*3326 + 1; hence not 2 divides 6653 by NAT_4:9;
    6653 = 3*2217 + 2; hence not 3 divides 6653 by NAT_4:9;
    6653 = 5*1330 + 3; hence not 5 divides 6653 by NAT_4:9;
    6653 = 7*950 + 3; hence not 7 divides 6653 by NAT_4:9;
    6653 = 11*604 + 9; hence not 11 divides 6653 by NAT_4:9;
    6653 = 13*511 + 10; hence not 13 divides 6653 by NAT_4:9;
    6653 = 17*391 + 6; hence not 17 divides 6653 by NAT_4:9;
    6653 = 19*350 + 3; hence not 19 divides 6653 by NAT_4:9;
    6653 = 23*289 + 6; hence not 23 divides 6653 by NAT_4:9;
    6653 = 29*229 + 12; hence not 29 divides 6653 by NAT_4:9;
    6653 = 31*214 + 19; hence not 31 divides 6653 by NAT_4:9;
    6653 = 37*179 + 30; hence not 37 divides 6653 by NAT_4:9;
    6653 = 41*162 + 11; hence not 41 divides 6653 by NAT_4:9;
    6653 = 43*154 + 31; hence not 43 divides 6653 by NAT_4:9;
    6653 = 47*141 + 26; hence not 47 divides 6653 by NAT_4:9;
    6653 = 53*125 + 28; hence not 53 divides 6653 by NAT_4:9;
    6653 = 59*112 + 45; hence not 59 divides 6653 by NAT_4:9;
    6653 = 61*109 + 4; hence not 61 divides 6653 by NAT_4:9;
    6653 = 67*99 + 20; hence not 67 divides 6653 by NAT_4:9;
    6653 = 71*93 + 50; hence not 71 divides 6653 by NAT_4:9;
    6653 = 73*91 + 10; hence not 73 divides 6653 by NAT_4:9;
    6653 = 79*84 + 17; hence not 79 divides 6653 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6653 & n is prime
  holds not n divides 6653 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
