
theorem
  6367 is prime
proof
  now
    6367 = 2*3183 + 1; hence not 2 divides 6367 by NAT_4:9;
    6367 = 3*2122 + 1; hence not 3 divides 6367 by NAT_4:9;
    6367 = 5*1273 + 2; hence not 5 divides 6367 by NAT_4:9;
    6367 = 7*909 + 4; hence not 7 divides 6367 by NAT_4:9;
    6367 = 11*578 + 9; hence not 11 divides 6367 by NAT_4:9;
    6367 = 13*489 + 10; hence not 13 divides 6367 by NAT_4:9;
    6367 = 17*374 + 9; hence not 17 divides 6367 by NAT_4:9;
    6367 = 19*335 + 2; hence not 19 divides 6367 by NAT_4:9;
    6367 = 23*276 + 19; hence not 23 divides 6367 by NAT_4:9;
    6367 = 29*219 + 16; hence not 29 divides 6367 by NAT_4:9;
    6367 = 31*205 + 12; hence not 31 divides 6367 by NAT_4:9;
    6367 = 37*172 + 3; hence not 37 divides 6367 by NAT_4:9;
    6367 = 41*155 + 12; hence not 41 divides 6367 by NAT_4:9;
    6367 = 43*148 + 3; hence not 43 divides 6367 by NAT_4:9;
    6367 = 47*135 + 22; hence not 47 divides 6367 by NAT_4:9;
    6367 = 53*120 + 7; hence not 53 divides 6367 by NAT_4:9;
    6367 = 59*107 + 54; hence not 59 divides 6367 by NAT_4:9;
    6367 = 61*104 + 23; hence not 61 divides 6367 by NAT_4:9;
    6367 = 67*95 + 2; hence not 67 divides 6367 by NAT_4:9;
    6367 = 71*89 + 48; hence not 71 divides 6367 by NAT_4:9;
    6367 = 73*87 + 16; hence not 73 divides 6367 by NAT_4:9;
    6367 = 79*80 + 47; hence not 79 divides 6367 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6367 & n is prime
  holds not n divides 6367 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
