
theorem
  6397 is prime
proof
  now
    6397 = 2*3198 + 1; hence not 2 divides 6397 by NAT_4:9;
    6397 = 3*2132 + 1; hence not 3 divides 6397 by NAT_4:9;
    6397 = 5*1279 + 2; hence not 5 divides 6397 by NAT_4:9;
    6397 = 7*913 + 6; hence not 7 divides 6397 by NAT_4:9;
    6397 = 11*581 + 6; hence not 11 divides 6397 by NAT_4:9;
    6397 = 13*492 + 1; hence not 13 divides 6397 by NAT_4:9;
    6397 = 17*376 + 5; hence not 17 divides 6397 by NAT_4:9;
    6397 = 19*336 + 13; hence not 19 divides 6397 by NAT_4:9;
    6397 = 23*278 + 3; hence not 23 divides 6397 by NAT_4:9;
    6397 = 29*220 + 17; hence not 29 divides 6397 by NAT_4:9;
    6397 = 31*206 + 11; hence not 31 divides 6397 by NAT_4:9;
    6397 = 37*172 + 33; hence not 37 divides 6397 by NAT_4:9;
    6397 = 41*156 + 1; hence not 41 divides 6397 by NAT_4:9;
    6397 = 43*148 + 33; hence not 43 divides 6397 by NAT_4:9;
    6397 = 47*136 + 5; hence not 47 divides 6397 by NAT_4:9;
    6397 = 53*120 + 37; hence not 53 divides 6397 by NAT_4:9;
    6397 = 59*108 + 25; hence not 59 divides 6397 by NAT_4:9;
    6397 = 61*104 + 53; hence not 61 divides 6397 by NAT_4:9;
    6397 = 67*95 + 32; hence not 67 divides 6397 by NAT_4:9;
    6397 = 71*90 + 7; hence not 71 divides 6397 by NAT_4:9;
    6397 = 73*87 + 46; hence not 73 divides 6397 by NAT_4:9;
    6397 = 79*80 + 77; hence not 79 divides 6397 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6397 & n is prime
  holds not n divides 6397 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
