Re: [math-fun] Car Talk and prime numbers
From: "Michael Kleber" <michael.kleber@gmail.com>
Phil Carmody wrote:
http://people.brandeis.edu/~kleber/temp/deletable.html """ Question: Why do prime bases (in red) seem to have many fewer deletable primes than composite bases? """
A much simpler, in fact trivial, question is: Why do odd bases seem to have many fewer deletable primes than even ones?
You're right, that does look like the right question to ask. When you say this is a trivial question, do you mean you know an answer, or just that it is easier to ask?
Yes. <stifles sniggering> Think of the problem of growing deletable primes by insertion, as in my script. If we have deletable prime P in base B and N digits in length, how many ways, ignoring duplication, are there to create a number one digit longer? If B was odd, how many of those ways yield an even number? And how many ways if B was even? Tada! Bob's your auntie's live-in lover. Wnen it comes to density of primes, is almost always explainable in terms of small prime divisors. This is no exception. Phil () ASCII ribbon campaign () Hopeless ribbon campaign /\ against HTML mail /\ against gratuitous bloodshed [stolen with permission from Daniel B. Cristofani] __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
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Phil Carmody