HP Prime CAS & Large numbers

[Joe Horn]

That's because floating-point numbers in Prime's CAS are limited to a maximum of roughly 10^308. Anything greater than that will be returned as infinity.

Examples:
2^1023.9999 --> 1.79756853259e308
2^1024. --> +Inf (notice the decimal point in the input)
2^1024 --> exact 309-digit answer

Here's a trick: If your CAS result is too big for CAS to convert to a real, but smaller than 500 digits, you can easily convert it to a real by importing it into Home. Just press Home, Menu (the physical Menu key), Get from CAS, then select the number. Unfortunately, your example, (256^256)*2^40, is too big even for Home to handle (it's 629 digits long). If you want to see how long it is, just use size(string(Ans)).

You can also use the following "biglog" program to return the common log of large CAS integers. It works with CAS integers of any size.

#cas
biglog(d):=
BEGIN
LOCAL j,k;
IF type(d)<>DOM_INT THEN RETURN "Argument not integer" END;
d:=abs(d);
k:=string(d);
j:=expr(head(k)+"."+tail(k));
return size(k)-1+evalf(log10(j),13);
END;
#end