
theorem
  8641 is prime
proof
  now
    8641 = 2*4320 + 1; hence not 2 divides 8641 by NAT_4:9;
    8641 = 3*2880 + 1; hence not 3 divides 8641 by NAT_4:9;
    8641 = 5*1728 + 1; hence not 5 divides 8641 by NAT_4:9;
    8641 = 7*1234 + 3; hence not 7 divides 8641 by NAT_4:9;
    8641 = 11*785 + 6; hence not 11 divides 8641 by NAT_4:9;
    8641 = 13*664 + 9; hence not 13 divides 8641 by NAT_4:9;
    8641 = 17*508 + 5; hence not 17 divides 8641 by NAT_4:9;
    8641 = 19*454 + 15; hence not 19 divides 8641 by NAT_4:9;
    8641 = 23*375 + 16; hence not 23 divides 8641 by NAT_4:9;
    8641 = 29*297 + 28; hence not 29 divides 8641 by NAT_4:9;
    8641 = 31*278 + 23; hence not 31 divides 8641 by NAT_4:9;
    8641 = 37*233 + 20; hence not 37 divides 8641 by NAT_4:9;
    8641 = 41*210 + 31; hence not 41 divides 8641 by NAT_4:9;
    8641 = 43*200 + 41; hence not 43 divides 8641 by NAT_4:9;
    8641 = 47*183 + 40; hence not 47 divides 8641 by NAT_4:9;
    8641 = 53*163 + 2; hence not 53 divides 8641 by NAT_4:9;
    8641 = 59*146 + 27; hence not 59 divides 8641 by NAT_4:9;
    8641 = 61*141 + 40; hence not 61 divides 8641 by NAT_4:9;
    8641 = 67*128 + 65; hence not 67 divides 8641 by NAT_4:9;
    8641 = 71*121 + 50; hence not 71 divides 8641 by NAT_4:9;
    8641 = 73*118 + 27; hence not 73 divides 8641 by NAT_4:9;
    8641 = 79*109 + 30; hence not 79 divides 8641 by NAT_4:9;
    8641 = 83*104 + 9; hence not 83 divides 8641 by NAT_4:9;
    8641 = 89*97 + 8; hence not 89 divides 8641 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8641 & n is prime
  holds not n divides 8641 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
