
theorem
  8039 is prime
proof
  now
    8039 = 2*4019 + 1; hence not 2 divides 8039 by NAT_4:9;
    8039 = 3*2679 + 2; hence not 3 divides 8039 by NAT_4:9;
    8039 = 5*1607 + 4; hence not 5 divides 8039 by NAT_4:9;
    8039 = 7*1148 + 3; hence not 7 divides 8039 by NAT_4:9;
    8039 = 11*730 + 9; hence not 11 divides 8039 by NAT_4:9;
    8039 = 13*618 + 5; hence not 13 divides 8039 by NAT_4:9;
    8039 = 17*472 + 15; hence not 17 divides 8039 by NAT_4:9;
    8039 = 19*423 + 2; hence not 19 divides 8039 by NAT_4:9;
    8039 = 23*349 + 12; hence not 23 divides 8039 by NAT_4:9;
    8039 = 29*277 + 6; hence not 29 divides 8039 by NAT_4:9;
    8039 = 31*259 + 10; hence not 31 divides 8039 by NAT_4:9;
    8039 = 37*217 + 10; hence not 37 divides 8039 by NAT_4:9;
    8039 = 41*196 + 3; hence not 41 divides 8039 by NAT_4:9;
    8039 = 43*186 + 41; hence not 43 divides 8039 by NAT_4:9;
    8039 = 47*171 + 2; hence not 47 divides 8039 by NAT_4:9;
    8039 = 53*151 + 36; hence not 53 divides 8039 by NAT_4:9;
    8039 = 59*136 + 15; hence not 59 divides 8039 by NAT_4:9;
    8039 = 61*131 + 48; hence not 61 divides 8039 by NAT_4:9;
    8039 = 67*119 + 66; hence not 67 divides 8039 by NAT_4:9;
    8039 = 71*113 + 16; hence not 71 divides 8039 by NAT_4:9;
    8039 = 73*110 + 9; hence not 73 divides 8039 by NAT_4:9;
    8039 = 79*101 + 60; hence not 79 divides 8039 by NAT_4:9;
    8039 = 83*96 + 71; hence not 83 divides 8039 by NAT_4:9;
    8039 = 89*90 + 29; hence not 89 divides 8039 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8039 & n is prime
  holds not n divides 8039 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
