Did you consider using other ways to select a page number?
One of the challenges of allowing a person to type into a field is they may not even type a number, so you will need to consider all sorts of other types of data entry field validation.
If you use an alternate way for selecting the page, which doesn't involve typing, then the person cannot enter incorrect characters, thus also simplifying the work for the developer and QA. However you would still have the conundrum of what to do with the Go button.
One alternative approach is to redesign the pagination. Consider this approach where you have a drop-down field and simple page forward and back buttons:
Because the user can see how many pages there are (1 of 6), they can simply press the Next button the number of times it takes to get to the page they want.
If you click the Page 1 of 6 drop-down you can display the following to help the user reach their intended page. Here I am display the Jump to page number (which defaults to the next page in the sequence) and the user simply toggles the page number up and down controls to change the number:
You can also see in this example, I am also allowing the user to choose how many items to display per pagination page, but I only included this as something else to think about.