
theorem
  8923 is prime
proof
  now
    8923 = 2*4461 + 1; hence not 2 divides 8923 by NAT_4:9;
    8923 = 3*2974 + 1; hence not 3 divides 8923 by NAT_4:9;
    8923 = 5*1784 + 3; hence not 5 divides 8923 by NAT_4:9;
    8923 = 7*1274 + 5; hence not 7 divides 8923 by NAT_4:9;
    8923 = 11*811 + 2; hence not 11 divides 8923 by NAT_4:9;
    8923 = 13*686 + 5; hence not 13 divides 8923 by NAT_4:9;
    8923 = 17*524 + 15; hence not 17 divides 8923 by NAT_4:9;
    8923 = 19*469 + 12; hence not 19 divides 8923 by NAT_4:9;
    8923 = 23*387 + 22; hence not 23 divides 8923 by NAT_4:9;
    8923 = 29*307 + 20; hence not 29 divides 8923 by NAT_4:9;
    8923 = 31*287 + 26; hence not 31 divides 8923 by NAT_4:9;
    8923 = 37*241 + 6; hence not 37 divides 8923 by NAT_4:9;
    8923 = 41*217 + 26; hence not 41 divides 8923 by NAT_4:9;
    8923 = 43*207 + 22; hence not 43 divides 8923 by NAT_4:9;
    8923 = 47*189 + 40; hence not 47 divides 8923 by NAT_4:9;
    8923 = 53*168 + 19; hence not 53 divides 8923 by NAT_4:9;
    8923 = 59*151 + 14; hence not 59 divides 8923 by NAT_4:9;
    8923 = 61*146 + 17; hence not 61 divides 8923 by NAT_4:9;
    8923 = 67*133 + 12; hence not 67 divides 8923 by NAT_4:9;
    8923 = 71*125 + 48; hence not 71 divides 8923 by NAT_4:9;
    8923 = 73*122 + 17; hence not 73 divides 8923 by NAT_4:9;
    8923 = 79*112 + 75; hence not 79 divides 8923 by NAT_4:9;
    8923 = 83*107 + 42; hence not 83 divides 8923 by NAT_4:9;
    8923 = 89*100 + 23; hence not 89 divides 8923 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8923 & n is prime
  holds not n divides 8923 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
