
Simple wave-optical superpositions as prime number sieves (2019) - Cieplak
https://arxiv.org/abs/1812.04203
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kurlberg
Low tech approach: Lehmer's bicycle chain sieve:

[https://en.wikipedia.org/wiki/Lehmer_sieve](https://en.wikipedia.org/wiki/Lehmer_sieve)

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Kednicma
I am reminded of two curious statements which are not normally linked:

(0) There could be a Siegel zero [0], like an "indentation" in the Riemann
zeta function. The prime numbers need to all collaborate to "shift" the zeta
function a little in order to "buckle" the zeta function at the Siegel zero,
so there's only really enough room in the primes to accomodate one Siegel zero
at most.

(1) Ultrafinitism [1] comes in many flavors, including a flavor where there is
a single largest prime number [2]. In this ultrafinite physical world, the
largest prime determines how large any object can be before folding back in on
itself. Since this would be a true statement about natural numbers, it would
also be a sort of conspiracy amongst the primes, with only one instance.

Situations like this article remind me of both simultaneously: If there's any
sort of conspiracy amongst the primes to forge a Siegel zero, it would have to
be the _same_ conspiracy which produces an ultrafinite prime candidate; the
primes don't have bandwidth for two conspiracies.

[0]
[https://en.wikipedia.org/wiki/Siegel_zero](https://en.wikipedia.org/wiki/Siegel_zero)

[1]
[https://en.wikipedia.org/wiki/Ultrafinitism](https://en.wikipedia.org/wiki/Ultrafinitism)

[2]
[https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/...](https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf)

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msla
> In this ultrafinite physical world, the largest prime determines how large
> any object can be before folding back in on itself.

This is why I don't like ultrafinitism: It insists on mixing levels, like an
Escher print.

The world of pure mathematics _isn 't_ the physical world, for all the same
reasons Santa Claus isn't real, and trying to bind pure math to some
(theoretical!) properties of the physical world is just as wrong-headed as
insisting that nobody can ever make songs about Santa because we know nobody
can deliver toys that quickly.

~~~
mensetmanusman
But it’s still a useful exercise, because at the interface where math does
seem to touch the real world, we can use it to make amazing predictions about
the behavior of future events.

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me_me_me
I tried to understand this paper but failed miserably, can anyone ELI5 for me?

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lordgrenville
Seconding this. My very basic understanding was that you propagate a wave with
a frequency of the first integer, then overlay another wave of the next, and
so on. As you go up, eventually the primes appear as the only place where they
interfere with each other completely so the wave is at 0.

~~~
posix_compliant
This is describing the sieve of eratosthenes! Very cool.

