Thought Experiment Time.......

[ToraToraTora]

OK we know that numbers are infinite, from this we can deduce that there is an infinite number of primes. So the question is.... Is the largest gap between prime numbers infinite or finite?

[JimF]

The prime gap, you mean? If so, it's explained well here:
https://en.wikipedia.org/wiki/Prime_gap

[Old_Geezer]

If there is always another prime up ahead, I'd vote that it must be finite. Unsure if infinity counts as a number let alone a prime. It's a concept. And comes in different flavours.

[ToraToraTora]

no one said infinity is a number or a prime.

[Old_Geezer]

It is implied, or even deduced, from the idea that it is in a number sequence that may have an infinite gap between it and the prior number.

[ClareTG0ld]

It's possible to construct arbitrarily large gaps between consecutive primes. It's difficult to know what the correct vocabulary is to describe this situation, because discussions about infinity often end up getting confusing, but "arbitrarily large" is I think the best way of putting it.

[bobbinwales]

i dont see how it can be infinite....a gap means to me that your talking about the difference between two finite numbers (yes they might be very big)

[douglas9401]

Finite, unlike the ego.

[Zacs-Master]

‘On average, the gap between a large prime p and the next prime number is approximately the natural logarithm of p, written log p. Number theorists long ago proved that there is no upper limit on how large the gap can grow, relative to log p’
https://www.science.org/content/article/mind-prime-gap#:~:text=On%20average%2C%20the%20gap%20between,grow%2C%20relative%20to%20log%20p.