
theorem
  9547 is prime
proof
  now
    9547 = 2*4773 + 1; hence not 2 divides 9547 by NAT_4:9;
    9547 = 3*3182 + 1; hence not 3 divides 9547 by NAT_4:9;
    9547 = 5*1909 + 2; hence not 5 divides 9547 by NAT_4:9;
    9547 = 7*1363 + 6; hence not 7 divides 9547 by NAT_4:9;
    9547 = 11*867 + 10; hence not 11 divides 9547 by NAT_4:9;
    9547 = 13*734 + 5; hence not 13 divides 9547 by NAT_4:9;
    9547 = 17*561 + 10; hence not 17 divides 9547 by NAT_4:9;
    9547 = 19*502 + 9; hence not 19 divides 9547 by NAT_4:9;
    9547 = 23*415 + 2; hence not 23 divides 9547 by NAT_4:9;
    9547 = 29*329 + 6; hence not 29 divides 9547 by NAT_4:9;
    9547 = 31*307 + 30; hence not 31 divides 9547 by NAT_4:9;
    9547 = 37*258 + 1; hence not 37 divides 9547 by NAT_4:9;
    9547 = 41*232 + 35; hence not 41 divides 9547 by NAT_4:9;
    9547 = 43*222 + 1; hence not 43 divides 9547 by NAT_4:9;
    9547 = 47*203 + 6; hence not 47 divides 9547 by NAT_4:9;
    9547 = 53*180 + 7; hence not 53 divides 9547 by NAT_4:9;
    9547 = 59*161 + 48; hence not 59 divides 9547 by NAT_4:9;
    9547 = 61*156 + 31; hence not 61 divides 9547 by NAT_4:9;
    9547 = 67*142 + 33; hence not 67 divides 9547 by NAT_4:9;
    9547 = 71*134 + 33; hence not 71 divides 9547 by NAT_4:9;
    9547 = 73*130 + 57; hence not 73 divides 9547 by NAT_4:9;
    9547 = 79*120 + 67; hence not 79 divides 9547 by NAT_4:9;
    9547 = 83*115 + 2; hence not 83 divides 9547 by NAT_4:9;
    9547 = 89*107 + 24; hence not 89 divides 9547 by NAT_4:9;
    9547 = 97*98 + 41; hence not 97 divides 9547 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9547 & n is prime
  holds not n divides 9547 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
