
theorem
  8171 is prime
proof
  now
    8171 = 2*4085 + 1; hence not 2 divides 8171 by NAT_4:9;
    8171 = 3*2723 + 2; hence not 3 divides 8171 by NAT_4:9;
    8171 = 5*1634 + 1; hence not 5 divides 8171 by NAT_4:9;
    8171 = 7*1167 + 2; hence not 7 divides 8171 by NAT_4:9;
    8171 = 11*742 + 9; hence not 11 divides 8171 by NAT_4:9;
    8171 = 13*628 + 7; hence not 13 divides 8171 by NAT_4:9;
    8171 = 17*480 + 11; hence not 17 divides 8171 by NAT_4:9;
    8171 = 19*430 + 1; hence not 19 divides 8171 by NAT_4:9;
    8171 = 23*355 + 6; hence not 23 divides 8171 by NAT_4:9;
    8171 = 29*281 + 22; hence not 29 divides 8171 by NAT_4:9;
    8171 = 31*263 + 18; hence not 31 divides 8171 by NAT_4:9;
    8171 = 37*220 + 31; hence not 37 divides 8171 by NAT_4:9;
    8171 = 41*199 + 12; hence not 41 divides 8171 by NAT_4:9;
    8171 = 43*190 + 1; hence not 43 divides 8171 by NAT_4:9;
    8171 = 47*173 + 40; hence not 47 divides 8171 by NAT_4:9;
    8171 = 53*154 + 9; hence not 53 divides 8171 by NAT_4:9;
    8171 = 59*138 + 29; hence not 59 divides 8171 by NAT_4:9;
    8171 = 61*133 + 58; hence not 61 divides 8171 by NAT_4:9;
    8171 = 67*121 + 64; hence not 67 divides 8171 by NAT_4:9;
    8171 = 71*115 + 6; hence not 71 divides 8171 by NAT_4:9;
    8171 = 73*111 + 68; hence not 73 divides 8171 by NAT_4:9;
    8171 = 79*103 + 34; hence not 79 divides 8171 by NAT_4:9;
    8171 = 83*98 + 37; hence not 83 divides 8171 by NAT_4:9;
    8171 = 89*91 + 72; hence not 89 divides 8171 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8171 & n is prime
  holds not n divides 8171 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
