
theorem
  9473 is prime
proof
  now
    9473 = 2*4736 + 1; hence not 2 divides 9473 by NAT_4:9;
    9473 = 3*3157 + 2; hence not 3 divides 9473 by NAT_4:9;
    9473 = 5*1894 + 3; hence not 5 divides 9473 by NAT_4:9;
    9473 = 7*1353 + 2; hence not 7 divides 9473 by NAT_4:9;
    9473 = 11*861 + 2; hence not 11 divides 9473 by NAT_4:9;
    9473 = 13*728 + 9; hence not 13 divides 9473 by NAT_4:9;
    9473 = 17*557 + 4; hence not 17 divides 9473 by NAT_4:9;
    9473 = 19*498 + 11; hence not 19 divides 9473 by NAT_4:9;
    9473 = 23*411 + 20; hence not 23 divides 9473 by NAT_4:9;
    9473 = 29*326 + 19; hence not 29 divides 9473 by NAT_4:9;
    9473 = 31*305 + 18; hence not 31 divides 9473 by NAT_4:9;
    9473 = 37*256 + 1; hence not 37 divides 9473 by NAT_4:9;
    9473 = 41*231 + 2; hence not 41 divides 9473 by NAT_4:9;
    9473 = 43*220 + 13; hence not 43 divides 9473 by NAT_4:9;
    9473 = 47*201 + 26; hence not 47 divides 9473 by NAT_4:9;
    9473 = 53*178 + 39; hence not 53 divides 9473 by NAT_4:9;
    9473 = 59*160 + 33; hence not 59 divides 9473 by NAT_4:9;
    9473 = 61*155 + 18; hence not 61 divides 9473 by NAT_4:9;
    9473 = 67*141 + 26; hence not 67 divides 9473 by NAT_4:9;
    9473 = 71*133 + 30; hence not 71 divides 9473 by NAT_4:9;
    9473 = 73*129 + 56; hence not 73 divides 9473 by NAT_4:9;
    9473 = 79*119 + 72; hence not 79 divides 9473 by NAT_4:9;
    9473 = 83*114 + 11; hence not 83 divides 9473 by NAT_4:9;
    9473 = 89*106 + 39; hence not 89 divides 9473 by NAT_4:9;
    9473 = 97*97 + 64; hence not 97 divides 9473 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9473 & n is prime
  holds not n divides 9473 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
