
theorem
  8089 is prime
proof
  now
    8089 = 2*4044 + 1; hence not 2 divides 8089 by NAT_4:9;
    8089 = 3*2696 + 1; hence not 3 divides 8089 by NAT_4:9;
    8089 = 5*1617 + 4; hence not 5 divides 8089 by NAT_4:9;
    8089 = 7*1155 + 4; hence not 7 divides 8089 by NAT_4:9;
    8089 = 11*735 + 4; hence not 11 divides 8089 by NAT_4:9;
    8089 = 13*622 + 3; hence not 13 divides 8089 by NAT_4:9;
    8089 = 17*475 + 14; hence not 17 divides 8089 by NAT_4:9;
    8089 = 19*425 + 14; hence not 19 divides 8089 by NAT_4:9;
    8089 = 23*351 + 16; hence not 23 divides 8089 by NAT_4:9;
    8089 = 29*278 + 27; hence not 29 divides 8089 by NAT_4:9;
    8089 = 31*260 + 29; hence not 31 divides 8089 by NAT_4:9;
    8089 = 37*218 + 23; hence not 37 divides 8089 by NAT_4:9;
    8089 = 41*197 + 12; hence not 41 divides 8089 by NAT_4:9;
    8089 = 43*188 + 5; hence not 43 divides 8089 by NAT_4:9;
    8089 = 47*172 + 5; hence not 47 divides 8089 by NAT_4:9;
    8089 = 53*152 + 33; hence not 53 divides 8089 by NAT_4:9;
    8089 = 59*137 + 6; hence not 59 divides 8089 by NAT_4:9;
    8089 = 61*132 + 37; hence not 61 divides 8089 by NAT_4:9;
    8089 = 67*120 + 49; hence not 67 divides 8089 by NAT_4:9;
    8089 = 71*113 + 66; hence not 71 divides 8089 by NAT_4:9;
    8089 = 73*110 + 59; hence not 73 divides 8089 by NAT_4:9;
    8089 = 79*102 + 31; hence not 79 divides 8089 by NAT_4:9;
    8089 = 83*97 + 38; hence not 83 divides 8089 by NAT_4:9;
    8089 = 89*90 + 79; hence not 89 divides 8089 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8089 & n is prime
  holds not n divides 8089 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
