
theorem
  9391 is prime
proof
  now
    9391 = 2*4695 + 1; hence not 2 divides 9391 by NAT_4:9;
    9391 = 3*3130 + 1; hence not 3 divides 9391 by NAT_4:9;
    9391 = 5*1878 + 1; hence not 5 divides 9391 by NAT_4:9;
    9391 = 7*1341 + 4; hence not 7 divides 9391 by NAT_4:9;
    9391 = 11*853 + 8; hence not 11 divides 9391 by NAT_4:9;
    9391 = 13*722 + 5; hence not 13 divides 9391 by NAT_4:9;
    9391 = 17*552 + 7; hence not 17 divides 9391 by NAT_4:9;
    9391 = 19*494 + 5; hence not 19 divides 9391 by NAT_4:9;
    9391 = 23*408 + 7; hence not 23 divides 9391 by NAT_4:9;
    9391 = 29*323 + 24; hence not 29 divides 9391 by NAT_4:9;
    9391 = 31*302 + 29; hence not 31 divides 9391 by NAT_4:9;
    9391 = 37*253 + 30; hence not 37 divides 9391 by NAT_4:9;
    9391 = 41*229 + 2; hence not 41 divides 9391 by NAT_4:9;
    9391 = 43*218 + 17; hence not 43 divides 9391 by NAT_4:9;
    9391 = 47*199 + 38; hence not 47 divides 9391 by NAT_4:9;
    9391 = 53*177 + 10; hence not 53 divides 9391 by NAT_4:9;
    9391 = 59*159 + 10; hence not 59 divides 9391 by NAT_4:9;
    9391 = 61*153 + 58; hence not 61 divides 9391 by NAT_4:9;
    9391 = 67*140 + 11; hence not 67 divides 9391 by NAT_4:9;
    9391 = 71*132 + 19; hence not 71 divides 9391 by NAT_4:9;
    9391 = 73*128 + 47; hence not 73 divides 9391 by NAT_4:9;
    9391 = 79*118 + 69; hence not 79 divides 9391 by NAT_4:9;
    9391 = 83*113 + 12; hence not 83 divides 9391 by NAT_4:9;
    9391 = 89*105 + 46; hence not 89 divides 9391 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9391 & n is prime
  holds not n divides 9391 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
