The problem is that nonstandard numbers behave like standard numbers from the inside.
Nonstandard numbers still have decimal representations, just the number of digits is nonstandard. They have prime factors, and some of them are prime.
We can look at it from the outside and say that its infinite, but from within, they behave just like very large finite numbers. In fact there is no formula in first order arithmatic, with 1 free variable, that is true on all standard numbers, and false on all nonstandard numbers.
The problem is that nonstandard numbers behave like standard numbers from the inside.
Nonstandard numbers still have decimal representations, just the number of digits is nonstandard. They have prime factors, and some of them are prime.
We can look at it from the outside and say that its infinite, but from within, they behave just like very large finite numbers. In fact there is no formula in first order arithmatic, with 1 free variable, that is true on all standard numbers, and false on all nonstandard numbers.