
theorem
  9377 is prime
proof
  now
    9377 = 2*4688 + 1; hence not 2 divides 9377 by NAT_4:9;
    9377 = 3*3125 + 2; hence not 3 divides 9377 by NAT_4:9;
    9377 = 5*1875 + 2; hence not 5 divides 9377 by NAT_4:9;
    9377 = 7*1339 + 4; hence not 7 divides 9377 by NAT_4:9;
    9377 = 11*852 + 5; hence not 11 divides 9377 by NAT_4:9;
    9377 = 13*721 + 4; hence not 13 divides 9377 by NAT_4:9;
    9377 = 17*551 + 10; hence not 17 divides 9377 by NAT_4:9;
    9377 = 19*493 + 10; hence not 19 divides 9377 by NAT_4:9;
    9377 = 23*407 + 16; hence not 23 divides 9377 by NAT_4:9;
    9377 = 29*323 + 10; hence not 29 divides 9377 by NAT_4:9;
    9377 = 31*302 + 15; hence not 31 divides 9377 by NAT_4:9;
    9377 = 37*253 + 16; hence not 37 divides 9377 by NAT_4:9;
    9377 = 41*228 + 29; hence not 41 divides 9377 by NAT_4:9;
    9377 = 43*218 + 3; hence not 43 divides 9377 by NAT_4:9;
    9377 = 47*199 + 24; hence not 47 divides 9377 by NAT_4:9;
    9377 = 53*176 + 49; hence not 53 divides 9377 by NAT_4:9;
    9377 = 59*158 + 55; hence not 59 divides 9377 by NAT_4:9;
    9377 = 61*153 + 44; hence not 61 divides 9377 by NAT_4:9;
    9377 = 67*139 + 64; hence not 67 divides 9377 by NAT_4:9;
    9377 = 71*132 + 5; hence not 71 divides 9377 by NAT_4:9;
    9377 = 73*128 + 33; hence not 73 divides 9377 by NAT_4:9;
    9377 = 79*118 + 55; hence not 79 divides 9377 by NAT_4:9;
    9377 = 83*112 + 81; hence not 83 divides 9377 by NAT_4:9;
    9377 = 89*105 + 32; hence not 89 divides 9377 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9377 & n is prime
  holds not n divides 9377 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
