
theorem
  8147 is prime
proof
  now
    8147 = 2*4073 + 1; hence not 2 divides 8147 by NAT_4:9;
    8147 = 3*2715 + 2; hence not 3 divides 8147 by NAT_4:9;
    8147 = 5*1629 + 2; hence not 5 divides 8147 by NAT_4:9;
    8147 = 7*1163 + 6; hence not 7 divides 8147 by NAT_4:9;
    8147 = 11*740 + 7; hence not 11 divides 8147 by NAT_4:9;
    8147 = 13*626 + 9; hence not 13 divides 8147 by NAT_4:9;
    8147 = 17*479 + 4; hence not 17 divides 8147 by NAT_4:9;
    8147 = 19*428 + 15; hence not 19 divides 8147 by NAT_4:9;
    8147 = 23*354 + 5; hence not 23 divides 8147 by NAT_4:9;
    8147 = 29*280 + 27; hence not 29 divides 8147 by NAT_4:9;
    8147 = 31*262 + 25; hence not 31 divides 8147 by NAT_4:9;
    8147 = 37*220 + 7; hence not 37 divides 8147 by NAT_4:9;
    8147 = 41*198 + 29; hence not 41 divides 8147 by NAT_4:9;
    8147 = 43*189 + 20; hence not 43 divides 8147 by NAT_4:9;
    8147 = 47*173 + 16; hence not 47 divides 8147 by NAT_4:9;
    8147 = 53*153 + 38; hence not 53 divides 8147 by NAT_4:9;
    8147 = 59*138 + 5; hence not 59 divides 8147 by NAT_4:9;
    8147 = 61*133 + 34; hence not 61 divides 8147 by NAT_4:9;
    8147 = 67*121 + 40; hence not 67 divides 8147 by NAT_4:9;
    8147 = 71*114 + 53; hence not 71 divides 8147 by NAT_4:9;
    8147 = 73*111 + 44; hence not 73 divides 8147 by NAT_4:9;
    8147 = 79*103 + 10; hence not 79 divides 8147 by NAT_4:9;
    8147 = 83*98 + 13; hence not 83 divides 8147 by NAT_4:9;
    8147 = 89*91 + 48; hence not 89 divides 8147 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8147 & n is prime
  holds not n divides 8147 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
