
theorem
  1553 is prime
proof
  now
    1553 = 2*776 + 1; hence not 2 divides 1553 by NAT_4:9;
    1553 = 3*517 + 2; hence not 3 divides 1553 by NAT_4:9;
    1553 = 5*310 + 3; hence not 5 divides 1553 by NAT_4:9;
    1553 = 7*221 + 6; hence not 7 divides 1553 by NAT_4:9;
    1553 = 11*141 + 2; hence not 11 divides 1553 by NAT_4:9;
    1553 = 13*119 + 6; hence not 13 divides 1553 by NAT_4:9;
    1553 = 17*91 + 6; hence not 17 divides 1553 by NAT_4:9;
    1553 = 19*81 + 14; hence not 19 divides 1553 by NAT_4:9;
    1553 = 23*67 + 12; hence not 23 divides 1553 by NAT_4:9;
    1553 = 29*53 + 16; hence not 29 divides 1553 by NAT_4:9;
    1553 = 31*50 + 3; hence not 31 divides 1553 by NAT_4:9;
    1553 = 37*41 + 36; hence not 37 divides 1553 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1553 & n is prime
  holds not n divides 1553 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
