
theorem
  8933 is prime
proof
  now
    8933 = 2*4466 + 1; hence not 2 divides 8933 by NAT_4:9;
    8933 = 3*2977 + 2; hence not 3 divides 8933 by NAT_4:9;
    8933 = 5*1786 + 3; hence not 5 divides 8933 by NAT_4:9;
    8933 = 7*1276 + 1; hence not 7 divides 8933 by NAT_4:9;
    8933 = 11*812 + 1; hence not 11 divides 8933 by NAT_4:9;
    8933 = 13*687 + 2; hence not 13 divides 8933 by NAT_4:9;
    8933 = 17*525 + 8; hence not 17 divides 8933 by NAT_4:9;
    8933 = 19*470 + 3; hence not 19 divides 8933 by NAT_4:9;
    8933 = 23*388 + 9; hence not 23 divides 8933 by NAT_4:9;
    8933 = 29*308 + 1; hence not 29 divides 8933 by NAT_4:9;
    8933 = 31*288 + 5; hence not 31 divides 8933 by NAT_4:9;
    8933 = 37*241 + 16; hence not 37 divides 8933 by NAT_4:9;
    8933 = 41*217 + 36; hence not 41 divides 8933 by NAT_4:9;
    8933 = 43*207 + 32; hence not 43 divides 8933 by NAT_4:9;
    8933 = 47*190 + 3; hence not 47 divides 8933 by NAT_4:9;
    8933 = 53*168 + 29; hence not 53 divides 8933 by NAT_4:9;
    8933 = 59*151 + 24; hence not 59 divides 8933 by NAT_4:9;
    8933 = 61*146 + 27; hence not 61 divides 8933 by NAT_4:9;
    8933 = 67*133 + 22; hence not 67 divides 8933 by NAT_4:9;
    8933 = 71*125 + 58; hence not 71 divides 8933 by NAT_4:9;
    8933 = 73*122 + 27; hence not 73 divides 8933 by NAT_4:9;
    8933 = 79*113 + 6; hence not 79 divides 8933 by NAT_4:9;
    8933 = 83*107 + 52; hence not 83 divides 8933 by NAT_4:9;
    8933 = 89*100 + 33; hence not 89 divides 8933 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8933 & n is prime
  holds not n divides 8933 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
