
theorem
  9337 is prime
proof
  now
    9337 = 2*4668 + 1; hence not 2 divides 9337 by NAT_4:9;
    9337 = 3*3112 + 1; hence not 3 divides 9337 by NAT_4:9;
    9337 = 5*1867 + 2; hence not 5 divides 9337 by NAT_4:9;
    9337 = 7*1333 + 6; hence not 7 divides 9337 by NAT_4:9;
    9337 = 11*848 + 9; hence not 11 divides 9337 by NAT_4:9;
    9337 = 13*718 + 3; hence not 13 divides 9337 by NAT_4:9;
    9337 = 17*549 + 4; hence not 17 divides 9337 by NAT_4:9;
    9337 = 19*491 + 8; hence not 19 divides 9337 by NAT_4:9;
    9337 = 23*405 + 22; hence not 23 divides 9337 by NAT_4:9;
    9337 = 29*321 + 28; hence not 29 divides 9337 by NAT_4:9;
    9337 = 31*301 + 6; hence not 31 divides 9337 by NAT_4:9;
    9337 = 37*252 + 13; hence not 37 divides 9337 by NAT_4:9;
    9337 = 41*227 + 30; hence not 41 divides 9337 by NAT_4:9;
    9337 = 43*217 + 6; hence not 43 divides 9337 by NAT_4:9;
    9337 = 47*198 + 31; hence not 47 divides 9337 by NAT_4:9;
    9337 = 53*176 + 9; hence not 53 divides 9337 by NAT_4:9;
    9337 = 59*158 + 15; hence not 59 divides 9337 by NAT_4:9;
    9337 = 61*153 + 4; hence not 61 divides 9337 by NAT_4:9;
    9337 = 67*139 + 24; hence not 67 divides 9337 by NAT_4:9;
    9337 = 71*131 + 36; hence not 71 divides 9337 by NAT_4:9;
    9337 = 73*127 + 66; hence not 73 divides 9337 by NAT_4:9;
    9337 = 79*118 + 15; hence not 79 divides 9337 by NAT_4:9;
    9337 = 83*112 + 41; hence not 83 divides 9337 by NAT_4:9;
    9337 = 89*104 + 81; hence not 89 divides 9337 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9337 & n is prime
  holds not n divides 9337 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
