Are there an infinite number of lucky primes?

Recomm. for undergrads: yes
Posted by: cubola zaruka
on: March 24th, 2010

\begin{conjecture} If every second positive integer except 2 is remaining, then every third remaining integer except 3, then every fourth remaining integer etc. , an infinite number of the remaining integers are prime. \end{conjecture}

The difference between the seive for generating primes and the seive for gnerating lucky numbers is that the former removes every nth integer whereas the latter removes every nth remaining integer. There are known to be an infinite number of lucky numbers because removing every nth remaining number leaves numbers unremoved as n increases and eventually becomes larger than any given value. There is also the unproved lucky analogue of the Goldbach conjecture, that every even number is expressible as the sum of two lucky numbers.


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