I have a question about prime numbers that might not have a proven

>>7727321
This gap you described has no bound, meaning that for every natural n there are two primes p,q with p-q>=n so that there is no prime number r with q<r<p.

>>7727321
That literally is the definition of a prime gap, [math]g_n = p_{n+1}-p_n[/math]
That gap increases to infinity. That doesn't mean there's a finite amount of primes, it just means it gets arbitrarily large for high n. Interestingly there's times when there's a huge gap between primes and then there's a twin prime right next to it.

Largefrac13fraclogXloglogXloglogloglogX(logloglogX)2

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Am I reading this correctly?

https://www.quantamagazine.org/20141210-prime-gap-grows-after-decades-long-lull/

is the implication here really that 70,000,000 is the largest possible gap indefinitely?

I must be reading it wrong, I thought the gap expanded to infinite

>>7727462
No the theorem states that we have a gap smaller than 70 mio infinitly often - ie the lim inf is bounded by that quantity. In fact we can prove a gap around 346 i think with Methods of Maynard and Tao. But something like 12 is the limit of that method so it will not prove prime twin conjecture. Its easy to see btw that you can create arbitrary long gaps by considering Numbers of the form x! + j with j = 1...x that will give you a gap of length x for any given x. There is also a conjucture about long gaps.

>>7727878
>No the the theoremes state´s that we have a gape smaler than the 70 mios infintely
No. can you restated
It¨s not cölesar English, please

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>>7727321
Hey I got a question for y'all

Does that recently formatted equation for sequencing primes include reducing irrationals to their infinitesimals?

;)

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>>7727321
tables of prime gaps

http://www.trnicely.net/index.html#TPG

>>7727348
It can't increase to infinity if it's a line segment on the number line. Two disparate points still = segment.

Though it is interesting to note that 333333... and 999999... are both infinite.

>>7727321
about 70 million.

there's a numberphile video about it

https://www.youtube.com/watch?v=vkMXdShDdtY

>>7728472
Although put into practical application that is some break the universe shit.

Unless we're thinking in terms of area. 3W x infinityL vs 9W x infinityL

It'd work for any dimensional space.

I guess that's one way of figuring that the energy of the universe can't be infinite. If the values of 333... and 999... were put into two separate mass forms Dear Lord Jesus

>>7728508
they were
in ur mum