Here is a number series: 41, 43, 47, 53, ...
arithmetic/prime.series New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
Here is a number series: 41, 43, 47, 53, ... 1. At what number does the series stop? 2. Why does it stop there? 3. What is additionally notable about the stopping point? 4. Are there any other similar series?
Show solution
Stop when the list contains 40 primes. n(k) = 41 + k*(k-1) is prime for k=1,2,...,40. The 41st number on the list would be 41*41, i.e., n(41) = 41*41. Neat! I didn't know this, but was vaguely aware that there are a few (simple?) functions known to produce primes on a restricted domain. You could probably find some of these with a good web search. -- soen <soen@pacbell.net> [ Editor: the puzzle was posted by NickGard, who wrote that he knew of one other such series; question 4 was not otherwise answered in the collected postings. ]