Answer: Mathematically there is no answer to this question, as the expression “biggest number in the world” is not well defined. There are various limits of size that have been put forward by mathematicians, but these limits only apply to specific domains, such as continuum mathematics or finite fields.

In any case, since you asked about integers strictly greater than zero, it would be an understatement to say that even a rough estimate of the number is beyond calculation! But…according to present-day cosmology there were roughly 1080 elementary particles created after the Big Bang and so even a rough estimate would probably be well over 10^(10^1080). I hope this satisfies your question! 🙂