
theorem
  9397 is prime
proof
  now
    9397 = 2*4698 + 1; hence not 2 divides 9397 by NAT_4:9;
    9397 = 3*3132 + 1; hence not 3 divides 9397 by NAT_4:9;
    9397 = 5*1879 + 2; hence not 5 divides 9397 by NAT_4:9;
    9397 = 7*1342 + 3; hence not 7 divides 9397 by NAT_4:9;
    9397 = 11*854 + 3; hence not 11 divides 9397 by NAT_4:9;
    9397 = 13*722 + 11; hence not 13 divides 9397 by NAT_4:9;
    9397 = 17*552 + 13; hence not 17 divides 9397 by NAT_4:9;
    9397 = 19*494 + 11; hence not 19 divides 9397 by NAT_4:9;
    9397 = 23*408 + 13; hence not 23 divides 9397 by NAT_4:9;
    9397 = 29*324 + 1; hence not 29 divides 9397 by NAT_4:9;
    9397 = 31*303 + 4; hence not 31 divides 9397 by NAT_4:9;
    9397 = 37*253 + 36; hence not 37 divides 9397 by NAT_4:9;
    9397 = 41*229 + 8; hence not 41 divides 9397 by NAT_4:9;
    9397 = 43*218 + 23; hence not 43 divides 9397 by NAT_4:9;
    9397 = 47*199 + 44; hence not 47 divides 9397 by NAT_4:9;
    9397 = 53*177 + 16; hence not 53 divides 9397 by NAT_4:9;
    9397 = 59*159 + 16; hence not 59 divides 9397 by NAT_4:9;
    9397 = 61*154 + 3; hence not 61 divides 9397 by NAT_4:9;
    9397 = 67*140 + 17; hence not 67 divides 9397 by NAT_4:9;
    9397 = 71*132 + 25; hence not 71 divides 9397 by NAT_4:9;
    9397 = 73*128 + 53; hence not 73 divides 9397 by NAT_4:9;
    9397 = 79*118 + 75; hence not 79 divides 9397 by NAT_4:9;
    9397 = 83*113 + 18; hence not 83 divides 9397 by NAT_4:9;
    9397 = 89*105 + 52; hence not 89 divides 9397 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9397 & n is prime
  holds not n divides 9397 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
