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Anonymous Fri 11 Feb 15:51:00 2022 No.14217594 View Reply Original Report

Quoted By: >>14217597 >>14218715 >>14218784

If prime numbers become less frequent as their value increases, AND there are infinite prime numbers, wouldn't they become infinitely infrequent at one point? Because they never stop losing frequency... EVER

Anonymous

Anonymous Fri 11 Feb 2022 15:52:09 No.14217597 Report

Quoted By: >>14217604 >>14218744

>>14217594
>wouldn't they become infinitely infrequent at one point?
no because the frequency never approaches zero

Anonymous

Anonymous Fri 11 Feb 2022 15:54:53 No.14217604 Report

Quoted By: >>14218590 >>14218739

>>14217597
To me it's like,

Pretend it's like this

3...5..7
And then the frequency changes to

11...15...19 etc.

It goes from 2 separation go 4 separation but the separation NEVER stops increasing so wouldn't it approach infinite separation then?

Anonymous

Anonymous Fri 11 Feb 2022 16:03:36 No.14217643 Report

Quoted By:

The cat is scared... Why?

Anonymous

Anonymous Fri 11 Feb 2022 20:45:12 No.14218590 Report

Quoted By:

>>14217604
The separation approaches infinity slower than the numbers approach infinity, so for any finite number there are primes greater than it.

Anonymous

Anonymous Fri 11 Feb 2022 21:17:24 No.14218715 Report

Quoted By:

>>14217594
Take every prime number and multiply them.
Add 1.
If it's prime, then you haven't picked the largest prime number.
If it's not prime, then you have taken every prime number.

What about the reverse, where primes are the ordinal, like 1st prime, 2nd prime, ... n prime, and that puts a bound on natural numbers? Natural numbers start repeating, or go backwards a little bit before they go forward? The infinite natural number is some function of the infinite prime number?

Anonymous

Anonymous Fri 11 Feb 2022 21:24:37 No.14218739 Report

Quoted By:

>>14217604
youre getting different sequences of infinites confused.

no element in the set of natural numbers is ever "infinity" it is always just another finite number and the difference between two finite numbers is always finite.

Anonymous

Anonymous Fri 11 Feb 2022 21:27:31 No.14218744 Report

Quoted By: >>14218755 >>14218777 >>14218796

>>14217597
>Frequency never approaches zero
How could you prove that?

Anonymous

Anonymous Fri 11 Feb 2022 21:31:35 No.14218755 Report

Quoted By:

>>14218744
You can always get a composite number by multiplying two primes, so the frequency can never be zero.

Anonymous

Anonymous Fri 11 Feb 2022 21:40:12 No.14218777 Report

Quoted By:

>>14218744
https://en.wikipedia.org/wiki/Euclid%27s_theorem
https://en.wikipedia.org/wiki/Prime_number_theorem
multiple ways. for example:

"Suppose to the contrary there are finite primes p1, p2, p3,...,pN. Let P=the product of all primes and q=P+1. Then, if q is not prime, then there certainly exists (by definition a prime number p that divides q. So, p must be in our list of p1, p2,...,pN which means it divides P and q simultaneously. Therefore it must divide the difference q-P=(P+1)-P=1 which is impossible since no prime divides 1. So finally, we must conclude p was not in our list of all primes. This is a contradiction, and the end of the proof that primes are innumerable."

Anonymous

Anonymous Fri 11 Feb 2022 21:42:08 No.14218784 Report

Quoted By:

>>14217594
why cant you guys wrap your heads around this?

Anonymous

Anonymous Fri 11 Feb 2022 21:46:08 No.14218796 Report

Quoted By:

>>14218744
given a finite collection of primes, there always exists another prime

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