
theorem
  9539 is prime
proof
  now
    9539 = 2*4769 + 1; hence not 2 divides 9539 by NAT_4:9;
    9539 = 3*3179 + 2; hence not 3 divides 9539 by NAT_4:9;
    9539 = 5*1907 + 4; hence not 5 divides 9539 by NAT_4:9;
    9539 = 7*1362 + 5; hence not 7 divides 9539 by NAT_4:9;
    9539 = 11*867 + 2; hence not 11 divides 9539 by NAT_4:9;
    9539 = 13*733 + 10; hence not 13 divides 9539 by NAT_4:9;
    9539 = 17*561 + 2; hence not 17 divides 9539 by NAT_4:9;
    9539 = 19*502 + 1; hence not 19 divides 9539 by NAT_4:9;
    9539 = 23*414 + 17; hence not 23 divides 9539 by NAT_4:9;
    9539 = 29*328 + 27; hence not 29 divides 9539 by NAT_4:9;
    9539 = 31*307 + 22; hence not 31 divides 9539 by NAT_4:9;
    9539 = 37*257 + 30; hence not 37 divides 9539 by NAT_4:9;
    9539 = 41*232 + 27; hence not 41 divides 9539 by NAT_4:9;
    9539 = 43*221 + 36; hence not 43 divides 9539 by NAT_4:9;
    9539 = 47*202 + 45; hence not 47 divides 9539 by NAT_4:9;
    9539 = 53*179 + 52; hence not 53 divides 9539 by NAT_4:9;
    9539 = 59*161 + 40; hence not 59 divides 9539 by NAT_4:9;
    9539 = 61*156 + 23; hence not 61 divides 9539 by NAT_4:9;
    9539 = 67*142 + 25; hence not 67 divides 9539 by NAT_4:9;
    9539 = 71*134 + 25; hence not 71 divides 9539 by NAT_4:9;
    9539 = 73*130 + 49; hence not 73 divides 9539 by NAT_4:9;
    9539 = 79*120 + 59; hence not 79 divides 9539 by NAT_4:9;
    9539 = 83*114 + 77; hence not 83 divides 9539 by NAT_4:9;
    9539 = 89*107 + 16; hence not 89 divides 9539 by NAT_4:9;
    9539 = 97*98 + 33; hence not 97 divides 9539 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9539 & n is prime
  holds not n divides 9539 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
