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Question: how does the density of R(x) primes, with respect to x, compare to the density of primes. Are they the same?
by quickthrower2 4y ago
Question: how does the density of R(x) primes, with respect to x, compare to the density of primes. Are they the same?
- Someone 4y agoWe don’t even know whether there are infinitely many decimal Repunit primes (https://primes.utm.edu/glossary/page.php?sort=Repunit https://primes.utm.edu/glossary/page.php?sort=Repunit) Even if that were true, we know there always is a prime between n and 2n (https://en.wikipedia.org/wiki/Bertrand%27s_postulate https://en.wikipedia.org/wiki/Bertrand%27s_postulate). Since there’s a factor of about 10 between successive repunits, the repunits themselves are already spaced further apart, let alone those that are prime (for which the first filter is “for R(x) to be prime, x must be prime”) So, no, they aren’t equal.
- quickthrower2 4y agoThanks for the answer. I meant with respect to x. So if R1 to R100 were all prime for example, for that range I consider it 100% dense by my definition. Instead if 0.0000000…00000009% dense by computing: 100/R100. Hope that makes sense. My definition of course may be at odds with mathematical conventions.
- deleted 4y ago[deleted]