
theorem
  8929 is prime
proof
  now
    8929 = 2*4464 + 1; hence not 2 divides 8929 by NAT_4:9;
    8929 = 3*2976 + 1; hence not 3 divides 8929 by NAT_4:9;
    8929 = 5*1785 + 4; hence not 5 divides 8929 by NAT_4:9;
    8929 = 7*1275 + 4; hence not 7 divides 8929 by NAT_4:9;
    8929 = 11*811 + 8; hence not 11 divides 8929 by NAT_4:9;
    8929 = 13*686 + 11; hence not 13 divides 8929 by NAT_4:9;
    8929 = 17*525 + 4; hence not 17 divides 8929 by NAT_4:9;
    8929 = 19*469 + 18; hence not 19 divides 8929 by NAT_4:9;
    8929 = 23*388 + 5; hence not 23 divides 8929 by NAT_4:9;
    8929 = 29*307 + 26; hence not 29 divides 8929 by NAT_4:9;
    8929 = 31*288 + 1; hence not 31 divides 8929 by NAT_4:9;
    8929 = 37*241 + 12; hence not 37 divides 8929 by NAT_4:9;
    8929 = 41*217 + 32; hence not 41 divides 8929 by NAT_4:9;
    8929 = 43*207 + 28; hence not 43 divides 8929 by NAT_4:9;
    8929 = 47*189 + 46; hence not 47 divides 8929 by NAT_4:9;
    8929 = 53*168 + 25; hence not 53 divides 8929 by NAT_4:9;
    8929 = 59*151 + 20; hence not 59 divides 8929 by NAT_4:9;
    8929 = 61*146 + 23; hence not 61 divides 8929 by NAT_4:9;
    8929 = 67*133 + 18; hence not 67 divides 8929 by NAT_4:9;
    8929 = 71*125 + 54; hence not 71 divides 8929 by NAT_4:9;
    8929 = 73*122 + 23; hence not 73 divides 8929 by NAT_4:9;
    8929 = 79*113 + 2; hence not 79 divides 8929 by NAT_4:9;
    8929 = 83*107 + 48; hence not 83 divides 8929 by NAT_4:9;
    8929 = 89*100 + 29; hence not 89 divides 8929 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8929 & n is prime
  holds not n divides 8929 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
