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From: "primenumbers Moderator" 
To:    therichardt@yahoo.com 

Subject: Welcome to primenumbers  
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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: TheRichardT@Yahoo.com 

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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