There is an alternate view whether prime numbers are infinite. It has to do with the word infinite itself.
The only aspect in our universe that is infinite is space. It has no borders. Everything else is limited.
Naturally, numbers aren't real. They are abstracts, so we find ourselves in the twilight zone of reality and abstract thinking. That's why there is an alternate answer.
When reviewing the actual actions associated with infinity, then we can see (quite easily actually) that the concept may exist forever, but that the contents peters out rather quickly.
Let's take an apple as example and cut it in half. Then, we cut the halves in half, and we continue to do so ad infinitum. In our brains, we can actually do that without much problem.
But in reality, the apple will have become apple sauce after twenty of such half-cuttings, and after fifty of such half-cuttings there may not even be any flavor left.
The concept lives on forever, but infinity is empty sooner rather than later.
That brings us to the prime numbers. When reviewing the number of prime numbers, I once calculated the number of primes in the first 1,000 spots, and the number of primes in the spots from (I hope I remember this number correctly) 10,000,000 to 11,000,000. In that section of 1,000,000 numbers there were fewer prime numbers than in the first 1,000 numbers.
It does not declare anything, but it does show how primes diminish greatly.
As such, it follows the natural pattern of matter, petering out before we know it.
The conclusion is that if we view prime numbers as an abstract, then -- in the abstract -- we can find a following prime number. But if we link numbers to reality (and make the numbers have a meaning), then there are no prime numbers of any consequence or of any meaning, sooner rather than later.
Not trying to make your article inconsequential. You did a great job and it shows how the human mind can stretch itself to great lengths. But the truth needs to be faced as well that the outcome of finding the next prime number is an exercise in futility.
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I discovered the prime number sequencing in 1992 and this was published in 2000, linking all spots for prime numbers in a single pattern.
