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To: "Paul Leyland" , "primenumbers" From: "Phil Carmody" | Block Address | Add to Address Book Date: Wed, 24 Apr 2002 00:35:51 -0700 (PDT) Subject: RE: [PrimeNumbers] What are they? Paul Leyland wrote: > > Paul L has a great example only in the integers. (I can't remember it). > > Philately will get you everywhere. Oi! stamp that out immmediately. The example you're probably thinking of is the set of even integers under the operations of arithmetic addition and multiplication. The set is infinite and closed under the operations in that for all a and b in the set, both a+b and a*b are also in the set. Here, 60 = 6*10 = 2*30 but none of 2, 6, 10 and 30 are divisible by any of the others. Note that the set is not a ring, or even a group under multiplication, as there is no multiplicative inverse. It has a 0, a non-0 element, is closed under addition, which is commutative, it is closed under multiplication, and multiplication is distributive over addition. What part of the definition of a ring are they missing? Phil

Subject: maths * 313 To: I just know that everyone will be impressed with the following "coincidences" concerning our good frend 313.... On page 313 of the Concord Desk Encyclopedia, the first sentence sez, "In 1933, ..." (it is an article about the concentration camps). 1933 is prime. In Websters Dictionary (Reference Library, paperback) on Page 313, the 313'th word is "arith" -- you have to count a bit sloppyily to get it come out correctly. But, still "It makes you think, doesn't it?" (spooky music in background). At EXACTLY 3 minutes and 13 seconds (3:13) into the first song on Frank Zappa's "Strictly Commercial" (best of) CD. There have been EXACTLY 3 minutes and 13 seconds of music played. (even spookier music in background) ;)
From: "Jud McCranie" Date: Tue, 23 Apr 2002 22:12:38 -0400 Subject: Re: [PrimeNumbers] phi(p)+sigma(p)=2p At 08:25 PM 4/23/2002 -0400, Jud McCranie wrote: > >You're right. Unless I made another mistake, the other direction can be proven by using the fact that sigma(n) > 6(n^2)/(pi^2*phi(n)) It looks like that proof fails. But you can use the formulas for phi and sigma. "Programming Achieved with Structure, Clarity, And Logic"

Twin Prime Trick puzzle

immediately, or don't at all. I was hoping that by restricting it to primes I could confuse a few people! (sqrt(7)+sqrt(5))^6 ~= 13535.995 (sqrt(13)+sqrt(11)^12 ~= 12103520127.9999997 (sqrt(19)+sqrt(17))^18 ~= 51638430914021375.99999999999 and so on. (Beware roundoff errors in your maths package - I've just seen calc produce some very awry answers, for example). Why do the primes separated by 2 follow this pattern, but primes separated by 4 not? rom: "Phil Carmody" Date: Tue, 23 Apr 2002 23:15:36 -0700 (PDT) Subject: Twin Prime trick puzzle --- Dan Morenus wrote: > Do *nonprimes* separated by 2 produce this pattern? I said it was a trick question, with sleight of hand, didn't I? Yup. Well spotted, primeness was indeed a red herring. Once you ignore primeness, it's a fairly easy question, but one of those things that you either see immediately, or don't at all. I was hoping that by restricting it to primes I could confuse a few people! Phil
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