
theorem
  8093 is prime
proof
  now
    8093 = 2*4046 + 1; hence not 2 divides 8093 by NAT_4:9;
    8093 = 3*2697 + 2; hence not 3 divides 8093 by NAT_4:9;
    8093 = 5*1618 + 3; hence not 5 divides 8093 by NAT_4:9;
    8093 = 7*1156 + 1; hence not 7 divides 8093 by NAT_4:9;
    8093 = 11*735 + 8; hence not 11 divides 8093 by NAT_4:9;
    8093 = 13*622 + 7; hence not 13 divides 8093 by NAT_4:9;
    8093 = 17*476 + 1; hence not 17 divides 8093 by NAT_4:9;
    8093 = 19*425 + 18; hence not 19 divides 8093 by NAT_4:9;
    8093 = 23*351 + 20; hence not 23 divides 8093 by NAT_4:9;
    8093 = 29*279 + 2; hence not 29 divides 8093 by NAT_4:9;
    8093 = 31*261 + 2; hence not 31 divides 8093 by NAT_4:9;
    8093 = 37*218 + 27; hence not 37 divides 8093 by NAT_4:9;
    8093 = 41*197 + 16; hence not 41 divides 8093 by NAT_4:9;
    8093 = 43*188 + 9; hence not 43 divides 8093 by NAT_4:9;
    8093 = 47*172 + 9; hence not 47 divides 8093 by NAT_4:9;
    8093 = 53*152 + 37; hence not 53 divides 8093 by NAT_4:9;
    8093 = 59*137 + 10; hence not 59 divides 8093 by NAT_4:9;
    8093 = 61*132 + 41; hence not 61 divides 8093 by NAT_4:9;
    8093 = 67*120 + 53; hence not 67 divides 8093 by NAT_4:9;
    8093 = 71*113 + 70; hence not 71 divides 8093 by NAT_4:9;
    8093 = 73*110 + 63; hence not 73 divides 8093 by NAT_4:9;
    8093 = 79*102 + 35; hence not 79 divides 8093 by NAT_4:9;
    8093 = 83*97 + 42; hence not 83 divides 8093 by NAT_4:9;
    8093 = 89*90 + 83; hence not 89 divides 8093 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8093 & n is prime
  holds not n divides 8093 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
