
theorem
  5573 is prime
proof
  now
    5573 = 2*2786 + 1; hence not 2 divides 5573 by NAT_4:9;
    5573 = 3*1857 + 2; hence not 3 divides 5573 by NAT_4:9;
    5573 = 5*1114 + 3; hence not 5 divides 5573 by NAT_4:9;
    5573 = 7*796 + 1; hence not 7 divides 5573 by NAT_4:9;
    5573 = 11*506 + 7; hence not 11 divides 5573 by NAT_4:9;
    5573 = 13*428 + 9; hence not 13 divides 5573 by NAT_4:9;
    5573 = 17*327 + 14; hence not 17 divides 5573 by NAT_4:9;
    5573 = 19*293 + 6; hence not 19 divides 5573 by NAT_4:9;
    5573 = 23*242 + 7; hence not 23 divides 5573 by NAT_4:9;
    5573 = 29*192 + 5; hence not 29 divides 5573 by NAT_4:9;
    5573 = 31*179 + 24; hence not 31 divides 5573 by NAT_4:9;
    5573 = 37*150 + 23; hence not 37 divides 5573 by NAT_4:9;
    5573 = 41*135 + 38; hence not 41 divides 5573 by NAT_4:9;
    5573 = 43*129 + 26; hence not 43 divides 5573 by NAT_4:9;
    5573 = 47*118 + 27; hence not 47 divides 5573 by NAT_4:9;
    5573 = 53*105 + 8; hence not 53 divides 5573 by NAT_4:9;
    5573 = 59*94 + 27; hence not 59 divides 5573 by NAT_4:9;
    5573 = 61*91 + 22; hence not 61 divides 5573 by NAT_4:9;
    5573 = 67*83 + 12; hence not 67 divides 5573 by NAT_4:9;
    5573 = 71*78 + 35; hence not 71 divides 5573 by NAT_4:9;
    5573 = 73*76 + 25; hence not 73 divides 5573 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5573 & n is prime
  holds not n divides 5573 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
