
theorem
  5569 is prime
proof
  now
    5569 = 2*2784 + 1; hence not 2 divides 5569 by NAT_4:9;
    5569 = 3*1856 + 1; hence not 3 divides 5569 by NAT_4:9;
    5569 = 5*1113 + 4; hence not 5 divides 5569 by NAT_4:9;
    5569 = 7*795 + 4; hence not 7 divides 5569 by NAT_4:9;
    5569 = 11*506 + 3; hence not 11 divides 5569 by NAT_4:9;
    5569 = 13*428 + 5; hence not 13 divides 5569 by NAT_4:9;
    5569 = 17*327 + 10; hence not 17 divides 5569 by NAT_4:9;
    5569 = 19*293 + 2; hence not 19 divides 5569 by NAT_4:9;
    5569 = 23*242 + 3; hence not 23 divides 5569 by NAT_4:9;
    5569 = 29*192 + 1; hence not 29 divides 5569 by NAT_4:9;
    5569 = 31*179 + 20; hence not 31 divides 5569 by NAT_4:9;
    5569 = 37*150 + 19; hence not 37 divides 5569 by NAT_4:9;
    5569 = 41*135 + 34; hence not 41 divides 5569 by NAT_4:9;
    5569 = 43*129 + 22; hence not 43 divides 5569 by NAT_4:9;
    5569 = 47*118 + 23; hence not 47 divides 5569 by NAT_4:9;
    5569 = 53*105 + 4; hence not 53 divides 5569 by NAT_4:9;
    5569 = 59*94 + 23; hence not 59 divides 5569 by NAT_4:9;
    5569 = 61*91 + 18; hence not 61 divides 5569 by NAT_4:9;
    5569 = 67*83 + 8; hence not 67 divides 5569 by NAT_4:9;
    5569 = 71*78 + 31; hence not 71 divides 5569 by NAT_4:9;
    5569 = 73*76 + 21; hence not 73 divides 5569 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5569 & n is prime
  holds not n divides 5569 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
