
theorem
  8117 is prime
proof
  now
    8117 = 2*4058 + 1; hence not 2 divides 8117 by NAT_4:9;
    8117 = 3*2705 + 2; hence not 3 divides 8117 by NAT_4:9;
    8117 = 5*1623 + 2; hence not 5 divides 8117 by NAT_4:9;
    8117 = 7*1159 + 4; hence not 7 divides 8117 by NAT_4:9;
    8117 = 11*737 + 10; hence not 11 divides 8117 by NAT_4:9;
    8117 = 13*624 + 5; hence not 13 divides 8117 by NAT_4:9;
    8117 = 17*477 + 8; hence not 17 divides 8117 by NAT_4:9;
    8117 = 19*427 + 4; hence not 19 divides 8117 by NAT_4:9;
    8117 = 23*352 + 21; hence not 23 divides 8117 by NAT_4:9;
    8117 = 29*279 + 26; hence not 29 divides 8117 by NAT_4:9;
    8117 = 31*261 + 26; hence not 31 divides 8117 by NAT_4:9;
    8117 = 37*219 + 14; hence not 37 divides 8117 by NAT_4:9;
    8117 = 41*197 + 40; hence not 41 divides 8117 by NAT_4:9;
    8117 = 43*188 + 33; hence not 43 divides 8117 by NAT_4:9;
    8117 = 47*172 + 33; hence not 47 divides 8117 by NAT_4:9;
    8117 = 53*153 + 8; hence not 53 divides 8117 by NAT_4:9;
    8117 = 59*137 + 34; hence not 59 divides 8117 by NAT_4:9;
    8117 = 61*133 + 4; hence not 61 divides 8117 by NAT_4:9;
    8117 = 67*121 + 10; hence not 67 divides 8117 by NAT_4:9;
    8117 = 71*114 + 23; hence not 71 divides 8117 by NAT_4:9;
    8117 = 73*111 + 14; hence not 73 divides 8117 by NAT_4:9;
    8117 = 79*102 + 59; hence not 79 divides 8117 by NAT_4:9;
    8117 = 83*97 + 66; hence not 83 divides 8117 by NAT_4:9;
    8117 = 89*91 + 18; hence not 89 divides 8117 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8117 & n is prime
  holds not n divides 8117 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
