
theorem
  9371 is prime
proof
  now
    9371 = 2*4685 + 1; hence not 2 divides 9371 by NAT_4:9;
    9371 = 3*3123 + 2; hence not 3 divides 9371 by NAT_4:9;
    9371 = 5*1874 + 1; hence not 5 divides 9371 by NAT_4:9;
    9371 = 7*1338 + 5; hence not 7 divides 9371 by NAT_4:9;
    9371 = 11*851 + 10; hence not 11 divides 9371 by NAT_4:9;
    9371 = 13*720 + 11; hence not 13 divides 9371 by NAT_4:9;
    9371 = 17*551 + 4; hence not 17 divides 9371 by NAT_4:9;
    9371 = 19*493 + 4; hence not 19 divides 9371 by NAT_4:9;
    9371 = 23*407 + 10; hence not 23 divides 9371 by NAT_4:9;
    9371 = 29*323 + 4; hence not 29 divides 9371 by NAT_4:9;
    9371 = 31*302 + 9; hence not 31 divides 9371 by NAT_4:9;
    9371 = 37*253 + 10; hence not 37 divides 9371 by NAT_4:9;
    9371 = 41*228 + 23; hence not 41 divides 9371 by NAT_4:9;
    9371 = 43*217 + 40; hence not 43 divides 9371 by NAT_4:9;
    9371 = 47*199 + 18; hence not 47 divides 9371 by NAT_4:9;
    9371 = 53*176 + 43; hence not 53 divides 9371 by NAT_4:9;
    9371 = 59*158 + 49; hence not 59 divides 9371 by NAT_4:9;
    9371 = 61*153 + 38; hence not 61 divides 9371 by NAT_4:9;
    9371 = 67*139 + 58; hence not 67 divides 9371 by NAT_4:9;
    9371 = 71*131 + 70; hence not 71 divides 9371 by NAT_4:9;
    9371 = 73*128 + 27; hence not 73 divides 9371 by NAT_4:9;
    9371 = 79*118 + 49; hence not 79 divides 9371 by NAT_4:9;
    9371 = 83*112 + 75; hence not 83 divides 9371 by NAT_4:9;
    9371 = 89*105 + 26; hence not 89 divides 9371 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9371 & n is prime
  holds not n divides 9371 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
