- Later today, hopefully, we at Riesel Sieve will announce the finding

of yet another prime. Weighing in at 661786 digits, it won't be the

largest for our project but a wonderful accomplishment none the less.

We are currently running a double check and will report it to Prime

Pages upon completion. So, I guess this is a warning to Chris

Caldwell also. VERY soon we will be killing your verification system

with a large prime:)

This will be the second 600k+ digit prime found in the month of May

this year for Riesel Sieve. As many know, I'm a firm believer in

numbers of a restricted form producing primes that seem to 'bunch'

together. Hopefully we will get yet another prime in before we hit

another 100+ day stretch of primeless search.

Lee Stephens

Riesel Sieve - On Tue, 2006-05-23 at 15:55, b2lee2003 wrote:

> this year for Riesel Sieve. As many know, I'm a firm believer in

If you believe that results of such searches occur at essentially random

> numbers of a restricted form producing primes that seem to 'bunch'

> together. Hopefully we will get yet another prime in before we hit

> another 100+ day stretch of primeless search.

intervals, this bunching behaviour is exactly what you should expect.

Read up on "Poisson statistics".

Paul

[Non-text portions of this message have been removed] - --- Paul Leyland <paul@...> wrote:
> On Tue, 2006-05-23 at 15:55, b2lee2003 wrote:

"Islands", they were once called. Some have mistakenly genuinely

> > this year for Riesel Sieve. As many know, I'm a firm believer in

> > numbers of a restricted form producing primes that seem to 'bunch'

> > together. Hopefully we will get yet another prime in before we hit

> > another 100+ day stretch of primeless search.

believed that they can be predicted. That was basically a re-working

of the "law of averages", which is basically assumes that things like

roulette tables, dice, or primes, have a memory. However, as Paul says:

> If you believe that results of such searches occur at essentially random

A great starter is to queue for a ride on the paradoxical Poisson bus:

> intervals, this bunching behaviour is exactly what you should expect.

> Read up on "Poisson statistics".

http://groups.yahoo.com/group/primenumbers/message/10356

(Which looks at the gaps rather than the hits themselves, but the maths

is the same.)

Phil, part of the Paul-Phil-prime-posting-partnership

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http://mail.yahoo.com - --- Phil Carmody wrote:
> A great starter is to queue for a ride on the paradoxical Poisson

Well put, Phil. ;^)

> bus:

>

> http://groups.yahoo.com/group/primenumbers/message/10356

Another interesting (and nonintuitive) fact about Poisson

distributions... Consider that bus stop which receives

an average of one bus per hour with Poisson distribution.

If you sample the gaps between buses over an extended period,

and round the result off to the nearest minute, what will be

the most-often-seen gap? Answer below...

The most often seen gap (when samples are rounded to the nearest

minute): 1 minute. Nowhere near the "intuitive" answer of

60 minutes.

That's a powerful argument for the existence of "prime islands"

and also a powerful argument against being able to predict them

(since they occur naturally as the result of a totally random

process).