
theorem
  8233 is prime
proof
  now
    8233 = 2*4116 + 1; hence not 2 divides 8233 by NAT_4:9;
    8233 = 3*2744 + 1; hence not 3 divides 8233 by NAT_4:9;
    8233 = 5*1646 + 3; hence not 5 divides 8233 by NAT_4:9;
    8233 = 7*1176 + 1; hence not 7 divides 8233 by NAT_4:9;
    8233 = 11*748 + 5; hence not 11 divides 8233 by NAT_4:9;
    8233 = 13*633 + 4; hence not 13 divides 8233 by NAT_4:9;
    8233 = 17*484 + 5; hence not 17 divides 8233 by NAT_4:9;
    8233 = 19*433 + 6; hence not 19 divides 8233 by NAT_4:9;
    8233 = 23*357 + 22; hence not 23 divides 8233 by NAT_4:9;
    8233 = 29*283 + 26; hence not 29 divides 8233 by NAT_4:9;
    8233 = 31*265 + 18; hence not 31 divides 8233 by NAT_4:9;
    8233 = 37*222 + 19; hence not 37 divides 8233 by NAT_4:9;
    8233 = 41*200 + 33; hence not 41 divides 8233 by NAT_4:9;
    8233 = 43*191 + 20; hence not 43 divides 8233 by NAT_4:9;
    8233 = 47*175 + 8; hence not 47 divides 8233 by NAT_4:9;
    8233 = 53*155 + 18; hence not 53 divides 8233 by NAT_4:9;
    8233 = 59*139 + 32; hence not 59 divides 8233 by NAT_4:9;
    8233 = 61*134 + 59; hence not 61 divides 8233 by NAT_4:9;
    8233 = 67*122 + 59; hence not 67 divides 8233 by NAT_4:9;
    8233 = 71*115 + 68; hence not 71 divides 8233 by NAT_4:9;
    8233 = 73*112 + 57; hence not 73 divides 8233 by NAT_4:9;
    8233 = 79*104 + 17; hence not 79 divides 8233 by NAT_4:9;
    8233 = 83*99 + 16; hence not 83 divides 8233 by NAT_4:9;
    8233 = 89*92 + 45; hence not 89 divides 8233 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8233 & n is prime
  holds not n divides 8233 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
