
theorem
  2333 is prime
proof
  now
    2333 = 2*1166 + 1; hence not 2 divides 2333 by NAT_4:9;
    2333 = 3*777 + 2; hence not 3 divides 2333 by NAT_4:9;
    2333 = 5*466 + 3; hence not 5 divides 2333 by NAT_4:9;
    2333 = 7*333 + 2; hence not 7 divides 2333 by NAT_4:9;
    2333 = 11*212 + 1; hence not 11 divides 2333 by NAT_4:9;
    2333 = 13*179 + 6; hence not 13 divides 2333 by NAT_4:9;
    2333 = 17*137 + 4; hence not 17 divides 2333 by NAT_4:9;
    2333 = 19*122 + 15; hence not 19 divides 2333 by NAT_4:9;
    2333 = 23*101 + 10; hence not 23 divides 2333 by NAT_4:9;
    2333 = 29*80 + 13; hence not 29 divides 2333 by NAT_4:9;
    2333 = 31*75 + 8; hence not 31 divides 2333 by NAT_4:9;
    2333 = 37*63 + 2; hence not 37 divides 2333 by NAT_4:9;
    2333 = 41*56 + 37; hence not 41 divides 2333 by NAT_4:9;
    2333 = 43*54 + 11; hence not 43 divides 2333 by NAT_4:9;
    2333 = 47*49 + 30; hence not 47 divides 2333 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2333 & n is prime
  holds not n divides 2333 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
