
theorem
  8647 is prime
proof
  now
    8647 = 2*4323 + 1; hence not 2 divides 8647 by NAT_4:9;
    8647 = 3*2882 + 1; hence not 3 divides 8647 by NAT_4:9;
    8647 = 5*1729 + 2; hence not 5 divides 8647 by NAT_4:9;
    8647 = 7*1235 + 2; hence not 7 divides 8647 by NAT_4:9;
    8647 = 11*786 + 1; hence not 11 divides 8647 by NAT_4:9;
    8647 = 13*665 + 2; hence not 13 divides 8647 by NAT_4:9;
    8647 = 17*508 + 11; hence not 17 divides 8647 by NAT_4:9;
    8647 = 19*455 + 2; hence not 19 divides 8647 by NAT_4:9;
    8647 = 23*375 + 22; hence not 23 divides 8647 by NAT_4:9;
    8647 = 29*298 + 5; hence not 29 divides 8647 by NAT_4:9;
    8647 = 31*278 + 29; hence not 31 divides 8647 by NAT_4:9;
    8647 = 37*233 + 26; hence not 37 divides 8647 by NAT_4:9;
    8647 = 41*210 + 37; hence not 41 divides 8647 by NAT_4:9;
    8647 = 43*201 + 4; hence not 43 divides 8647 by NAT_4:9;
    8647 = 47*183 + 46; hence not 47 divides 8647 by NAT_4:9;
    8647 = 53*163 + 8; hence not 53 divides 8647 by NAT_4:9;
    8647 = 59*146 + 33; hence not 59 divides 8647 by NAT_4:9;
    8647 = 61*141 + 46; hence not 61 divides 8647 by NAT_4:9;
    8647 = 67*129 + 4; hence not 67 divides 8647 by NAT_4:9;
    8647 = 71*121 + 56; hence not 71 divides 8647 by NAT_4:9;
    8647 = 73*118 + 33; hence not 73 divides 8647 by NAT_4:9;
    8647 = 79*109 + 36; hence not 79 divides 8647 by NAT_4:9;
    8647 = 83*104 + 15; hence not 83 divides 8647 by NAT_4:9;
    8647 = 89*97 + 14; hence not 89 divides 8647 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8647 & n is prime
  holds not n divides 8647 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
