
theorem
  5399 is prime
proof
  now
    5399 = 2*2699 + 1; hence not 2 divides 5399 by NAT_4:9;
    5399 = 3*1799 + 2; hence not 3 divides 5399 by NAT_4:9;
    5399 = 5*1079 + 4; hence not 5 divides 5399 by NAT_4:9;
    5399 = 7*771 + 2; hence not 7 divides 5399 by NAT_4:9;
    5399 = 11*490 + 9; hence not 11 divides 5399 by NAT_4:9;
    5399 = 13*415 + 4; hence not 13 divides 5399 by NAT_4:9;
    5399 = 17*317 + 10; hence not 17 divides 5399 by NAT_4:9;
    5399 = 19*284 + 3; hence not 19 divides 5399 by NAT_4:9;
    5399 = 23*234 + 17; hence not 23 divides 5399 by NAT_4:9;
    5399 = 29*186 + 5; hence not 29 divides 5399 by NAT_4:9;
    5399 = 31*174 + 5; hence not 31 divides 5399 by NAT_4:9;
    5399 = 37*145 + 34; hence not 37 divides 5399 by NAT_4:9;
    5399 = 41*131 + 28; hence not 41 divides 5399 by NAT_4:9;
    5399 = 43*125 + 24; hence not 43 divides 5399 by NAT_4:9;
    5399 = 47*114 + 41; hence not 47 divides 5399 by NAT_4:9;
    5399 = 53*101 + 46; hence not 53 divides 5399 by NAT_4:9;
    5399 = 59*91 + 30; hence not 59 divides 5399 by NAT_4:9;
    5399 = 61*88 + 31; hence not 61 divides 5399 by NAT_4:9;
    5399 = 67*80 + 39; hence not 67 divides 5399 by NAT_4:9;
    5399 = 71*76 + 3; hence not 71 divides 5399 by NAT_4:9;
    5399 = 73*73 + 70; hence not 73 divides 5399 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5399 & n is prime
  holds not n divides 5399 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
