
theorem
  6389 is prime
proof
  now
    6389 = 2*3194 + 1; hence not 2 divides 6389 by NAT_4:9;
    6389 = 3*2129 + 2; hence not 3 divides 6389 by NAT_4:9;
    6389 = 5*1277 + 4; hence not 5 divides 6389 by NAT_4:9;
    6389 = 7*912 + 5; hence not 7 divides 6389 by NAT_4:9;
    6389 = 11*580 + 9; hence not 11 divides 6389 by NAT_4:9;
    6389 = 13*491 + 6; hence not 13 divides 6389 by NAT_4:9;
    6389 = 17*375 + 14; hence not 17 divides 6389 by NAT_4:9;
    6389 = 19*336 + 5; hence not 19 divides 6389 by NAT_4:9;
    6389 = 23*277 + 18; hence not 23 divides 6389 by NAT_4:9;
    6389 = 29*220 + 9; hence not 29 divides 6389 by NAT_4:9;
    6389 = 31*206 + 3; hence not 31 divides 6389 by NAT_4:9;
    6389 = 37*172 + 25; hence not 37 divides 6389 by NAT_4:9;
    6389 = 41*155 + 34; hence not 41 divides 6389 by NAT_4:9;
    6389 = 43*148 + 25; hence not 43 divides 6389 by NAT_4:9;
    6389 = 47*135 + 44; hence not 47 divides 6389 by NAT_4:9;
    6389 = 53*120 + 29; hence not 53 divides 6389 by NAT_4:9;
    6389 = 59*108 + 17; hence not 59 divides 6389 by NAT_4:9;
    6389 = 61*104 + 45; hence not 61 divides 6389 by NAT_4:9;
    6389 = 67*95 + 24; hence not 67 divides 6389 by NAT_4:9;
    6389 = 71*89 + 70; hence not 71 divides 6389 by NAT_4:9;
    6389 = 73*87 + 38; hence not 73 divides 6389 by NAT_4:9;
    6389 = 79*80 + 69; hence not 79 divides 6389 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6389 & n is prime
  holds not n divides 6389 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
