I am reminded of two curious statements which are not normally linked:<p>(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.<p>(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.<p>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 <i>same</i> conspiracy which produces an ultrafinite prime candidate; the primes don't have bandwidth for two conspiracies.<p>[0] <a href="https://en.wikipedia.org/wiki/Siegel_zero" rel="nofollow">https://en.wikipedia.org/wiki/Siegel_zero</a><p>[1] <a href="https://en.wikipedia.org/wiki/Ultrafinitism" rel="nofollow">https://en.wikipedia.org/wiki/Ultrafinitism</a><p>[2] <a href="https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf" rel="nofollow">https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/...</a>