## Fw: {Spam?} [PrimeNumbers] the 357 rule

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• forwarded... ... From: Bill Bouris To: Paul Leyland Sent: Mon, February 1, 2010 8:42:15 AM Subject: Re: {Spam?}
Message 1 of 3 , Feb 1, 2010
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----- Forwarded Message ----
From: Bill Bouris <leavemsg1@...>
To: Paul Leyland <paul@...>
Sent: Mon, February 1, 2010 8:42:15 AM
Subject: Re: {Spam?} [PrimeNumbers] the 357 rule

not a complete craptrap... I was going to say that if it were false, that a simple
3-PRP would expose those numbers that did not have that property.

----- Original Message ----
From: Paul Leyland <paul@...>
To: Bill Bouris <leavemsg1@...>
Sent: Mon, February 1, 2010 8:39:10 AM
Subject: Re: {Spam?} [PrimeNumbers] the 357 rule

Aargh!  I misunderstood the example and posted complete claptrap.  My
apologies.

To make amends: all Fermat numbers pass the 2-PRP test.  Many composite
Fermat numbers N are known and all are divisible only by integers larger
that 7.  In every case, N is a power of 2, by definition, and so not
divisible by 3, 5, 7.

Paul

On Mon, 2010-02-01 at 14:34 +0000, Paul Leyland wrote:
> If you used your elderly computer to search for known results rather
> than for computations you would have discovered
> http://www.research.att.com/~njas/sequences/A055550 and, in particular,
> the entry 264239
>
> 264239 = 139 * 1901
> 264238 = 2 * 13 * 10163
>
>
> Paul
>
>
> On Mon, 2010-02-01 at 06:18 -0800, Bill Bouris wrote:
> >
> > Group,
> > I believe that if 'N' passes the 2-PRP test that either 3, 5, or 7
> > divides 'N-1', one or
> > all of them, or 'N' will be divisible by 3, 5, or 7 and be composite.
> > I could only go
> > so far with my outdated computer and UBasic. Can anyone find a
> > counter-example ???
> > Bill
> >
> >
> >
> >
> >
• ... n = 1097343303233 is not prime n is 2-PRP n is 3-PRP n is coprime to 3*5*7 n-1 is coprime to 3*5*7 There are 95 such counterexamples in
Message 2 of 3 , Feb 1, 2010
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Bill Bouris <leavemsg1@...> wrote:

> I was going to say that if it were false
> that a simple 3-PRP would expose those
> numbers that did not have that property

n = 1097343303233 is not prime
n is 2-PRP
n is 3-PRP
n is coprime to 3*5*7
n-1 is coprime to 3*5*7

There are 95 such counterexamples in