
theorem
  6089 is prime
proof
  now
    6089 = 2*3044 + 1; hence not 2 divides 6089 by NAT_4:9;
    6089 = 3*2029 + 2; hence not 3 divides 6089 by NAT_4:9;
    6089 = 5*1217 + 4; hence not 5 divides 6089 by NAT_4:9;
    6089 = 7*869 + 6; hence not 7 divides 6089 by NAT_4:9;
    6089 = 11*553 + 6; hence not 11 divides 6089 by NAT_4:9;
    6089 = 13*468 + 5; hence not 13 divides 6089 by NAT_4:9;
    6089 = 17*358 + 3; hence not 17 divides 6089 by NAT_4:9;
    6089 = 19*320 + 9; hence not 19 divides 6089 by NAT_4:9;
    6089 = 23*264 + 17; hence not 23 divides 6089 by NAT_4:9;
    6089 = 29*209 + 28; hence not 29 divides 6089 by NAT_4:9;
    6089 = 31*196 + 13; hence not 31 divides 6089 by NAT_4:9;
    6089 = 37*164 + 21; hence not 37 divides 6089 by NAT_4:9;
    6089 = 41*148 + 21; hence not 41 divides 6089 by NAT_4:9;
    6089 = 43*141 + 26; hence not 43 divides 6089 by NAT_4:9;
    6089 = 47*129 + 26; hence not 47 divides 6089 by NAT_4:9;
    6089 = 53*114 + 47; hence not 53 divides 6089 by NAT_4:9;
    6089 = 59*103 + 12; hence not 59 divides 6089 by NAT_4:9;
    6089 = 61*99 + 50; hence not 61 divides 6089 by NAT_4:9;
    6089 = 67*90 + 59; hence not 67 divides 6089 by NAT_4:9;
    6089 = 71*85 + 54; hence not 71 divides 6089 by NAT_4:9;
    6089 = 73*83 + 30; hence not 73 divides 6089 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6089 & n is prime
  holds not n divides 6089 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
