Re: [math-fun] Origins of a problem.
there is an old problem in which one asks that the integers from 1 to N be listed so that the sum of adjacent integers are primes. I've never seen a solution. It is probably true that one can always do this with N at the end of the list. if one knew that for N>9 there is always a pair of twin primes betwen N and 2N all of this would follow. But there should be a real proof. anyone know anything?
At 11:09 PM 11/19/2002 -0500, you wrote:
there is an old problem in which one asks that the integers from 1 to N be listed so that the sum of adjacent integers are primes. I've never seen a solution. It is probably true that one can always do this with N at the end of the list.
if one knew that for N>9 there is always a pair of twin primes betwen N and 2N all of this would follow. But there should be a real proof.
anyone know anything?
I believe I've seen it on www.primepuzzles.net See Primes in a circle: http://www.primepuzzles.net/puzzles/puzz_176.htm +---------------------------------------------------------+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +---------------------------------------------------------+
I wrote an article `Prime Pyramids' in Crux Math, 19(1993) 97-99, based on a proposal of Margaret J Kenney of Boston College in the Student Math Notes enclosed with the Nov 1986 NCTM News Bulletin. I gave heuristic arguments which I thought that a good technician might be able to formalize into a proof, but I haven't seen one. R. On Tue, 19 Nov 2002 POPPY9X@aol.com wrote:
there is an old problem in which one asks that the integers from 1 to N be listed so that the sum of adjacent integers are primes. I've never seen a solution. It is probably true that one can always do this with N at the end of the list.
if one knew that for N>9 there is always a pair of twin primes betwen N and 2N all of this would follow. But there should be a real proof.
anyone know anything?
participants (3)
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Jud McCranie -
POPPY9X＠aol.com -
Richard Guy