[Math] the largest known prime gap, and why is there so much conflicting information?

prime numbersprime-gaps

I find consistently conflicting information online.

On the one hand there's all these reports of the largest prime gap between all numbers proven to be < 246.

On the other hand, I read reports of the largest known prime number gap being 1476.

On the other hand, I find all kind of different reports, such as this one: http://sweet.ua.pt/tos/gaps.html where there are many prime numbers with gaps > 246.

What am I failing to understand?

Thanks!

EDIT: There's many good answers on this page. Thanks so much you guys! I only chose dalastboss's because I found it easiest to grasp. It was 'dumbed down' enough for me 🙂

Best Answer

For every number $n\in\mathbb{N}$ that you can think of, I can give you a sequence of $n-1$ consecutive numbers, none of which is prime.

There you go: $n!+2,n!+3,\dots,n!+n$.

So there is no finite bound on the gap between two consecutive primes.