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Hello,
This appears to be a nice group. I have an interest in primes, so
I thought I would contribute. What a coincidence, I appear to have
the same handle as paulmillscv. C'est la vie! But I have noticed
one thing, why does D Broadhurst pretend not to understand my
namesake's contributions? Surely they both have Ph.Ds? Can someone
remind him that it is quite alright to do the dirty on a fellow
countryman at home but decidedly not British to do it on an
International Public List. There is such a thing as British
Justice. Although I thought that `your honour' handing out 26 life
sentences the other day was slightly OTT. A couple would have done.
Basically, lose the instant email graffiti David, think first then
think.
The LHS is always an integer, the RHS (Faulhaber formulae) is .. the
RHS, call it n(a/b) if you want. But for sure it is not an integer
all the time. That is the contradiction. Therefore the equality is
false, therefore it has no solution at any time.
If you wish more light on the proof wrt to the Faulhaber formulae,
then ask Donald Knuth. Phil, please tell me a good joke. Thank you.
Regards,
Paul Mills,
Kenilworth,
England. 0 Attachment
On Thu, 21 February 2002, "paulmillscv" wrote:> Hello,
Heh, until it let me in :).
> This appears to be a nice group.
> I have an interest in primes, so
Robert Harley would be asking where the bits are by now (FoRK reference).
> I thought I would contribute. What a coincidence, I appear to have
> the same handle as paulmillscv. C'est la vie!
> But I have noticed
To be able to parse the syntax in a post, detect that semantically it does not follow the traditional rules of mathematical deduction, and say so in a lucid, if blunt, fashion is _not_ what I'd call "not understanding".
> one thing, why does D Broadhurst pretend not to understand my
> namesake's contributions?
> Surely they both have Ph.Ds?
Irrelevant. Anyway, I'd rather have philalethy than philosophy.
> Can someone
Again, where are the bits? (I'm looking for information content, you see.)
> remind him that it is quite alright to do the dirty on a fellow
> countryman at home but decidedly not British to do it on an
> International Public List. There is such a thing as British
> Justice. Although I thought that `your honour' handing out 26 life
> sentences the other day was slightly OTT. A couple would have done.
> Basically, lose the instant email graffiti David, think first then
My mote detector needle may have just twitched.
> think.
> The LHS is always an integer, the RHS (Faulhaber formulae) is .. the
Maybe the more classically educated here will remind me what school of philosophy uses "for sure" as its basic underpinning.
> RHS, call it n(a/b) if you want. But for sure it is not an integer
> all the time.
> That is the contradiction. Therefore the equality is
Hmmm, I've not got past the "for sure" bit yet  what part in which syllogism does it play?
> false,
> therefore it has no solution at any time.
Woh! It looks like you're saying
NOT(\forall a \in A f(a)=g(a))  \forall a \in A NOT(f(a)=f(b))
I think you need to take your '' operator back to the store where you bought it, and get your money back.
> If you wish more light on the proof wrt to the Faulhaber formulae,
Oooh, I may not have any letters afer my name (apart from the courtesy 'Esq.'), but I _do_ have a $5.12 cheque from one Donald Knuth, hand signed (with a felt tip pen by the looks of it!).
> then ask Donald Knuth. Phil, please tell me a good joke. Thank you.
Anyway, there was this large negative epsilon...
Phil
Don't be fooled, CRC Press are _not_ the good guys.
They've taken Wolfram's money  _don't_ give them yours.
http://mathworld.wolfram.com/erics_commentary.html
Find the best deals on the web at AltaVista Shopping!
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Hi,
> This appears to be a nice group.
It once was  the signal to noise ratio has been decreasing for years
though.
> Surely they both have Ph.Ds?
Why are people so hung up on what letters they have after their names?
Surely it is whether you can make interesting contributions that matters.
> Basically, lose the instant email graffiti David, think first then
While David is sometimes blunt, he is very rarely wrong, and when he is he
> think.
graciously accepts the correction and moves on. What is becoming
increasingly annoying on this list is when someone points out a problem in a
"proof" and all the person who claimed the "proof" does is reiterate what
they said in the first place, rather than either try to point out why the
argument used against their proof is incorrect, rework the proof or admit
they were wrong and couldn't in fact prove it.
What's even worse is people sometimes appear to realise they can't justify
their proof and just launch a personal attack on the member of the list that
pointed out the problem. Please, could we stick to maths?
On that note, I'd like to announce the discovery of a record quadruplet:
10271674954.3000#+3461
10271674954.3000#+3463
10271674954.3000#+3467
10271674954.3000#+3469 (1284 digits)
proved prime by Primo, PRP tested using PFGW, sieved using APSieve. PRP
testing was done by the following people: Michael Bell, Michael Davison,
Matt Jack, Ronald Lau, Graeme Leese and Benjamin Lowing.
Sorry for the above noise,
Michael.
P.S. Chris: I don't seem to be able to submit these using the web entry
form, is it because 3000 isn't prime? 0 Attachment
> Oooh, I may not have any letters afer my name (apart from the
Ooh, name dropping, eh?
> courtesy 'Esq.'), but I _do_ have a $5.12 cheque from one
> Donald Knuth, hand signed (with a felt tip pen by the looks of it!).
Seeing that you raised the topic, let's see if anyone else here wants to
admit to having a Knuth check (note spelling, he's American drawing
checks in US dollars). Mine is for $2.88 so yours trumps mine but
"never mind the width, feel the quality" is what I say. I deduce you
sent in two bugs whereas mine was one bug (in an attempted bug
correction no less) and a suggestion.
Erdos numbers anyone? I can only manage a 2. There must be some on the
list with a 1.
Paul 0 Attachment
Hello Phil,
Thank you for increasing the wit quotient in the last few
posts. Before anyone posts a negative number they should ask
themselves, just exactly how many people in my neighbourhood, town,
country,hemisphere know what quadratic reciprocity is? The people on
this list are generally off the scale when it comes to IQ. So treat
them as such and they will respond in turn. The method of descent
is preferable to the method of dissent. Life is poetry, poetry is
life. Basically, there is plenty of truth, fame, rewards for all
potential number theorists, I should know because being one of the
top ten number theorists in the UK I know what it feels like.
Regards,
Paul Mills
Kenilworth,
England.
 In primenumbers@y..., Phil Carmody <fatphil@a...> wrote:
> On Thu, 21 February 2002, "paulmillscv" wrote:
> > Hello,
> > This appears to be a nice group.
>
> Heh, until it let me in :).
>
> > I have an interest in primes, so
> > I thought I would contribute. What a coincidence, I appear to
have
> > the same handle as paulmillscv. C'est la vie!
>
> Robert Harley would be asking where the bits are by now (FoRK
reference).
>
> > But I have noticed
> > one thing, why does D Broadhurst pretend not to understand my
> > namesake's contributions?
>
> To be able to parse the syntax in a post, detect that semantically
it does not follow the traditional rules of mathematical deduction,
and say so in a lucid, if blunt, fashion is _not_ what I'd call "not
understanding".
>
> > Surely they both have Ph.Ds?
>
> Irrelevant. Anyway, I'd rather have philalethy than philosophy.
>
> > Can someone
> > remind him that it is quite alright to do the dirty on a fellow
> > countryman at home but decidedly not British to do it on an
> > International Public List. There is such a thing as British
> > Justice. Although I thought that `your honour' handing out 26
life
> > sentences the other day was slightly OTT. A couple would have
done.
>
> Again, where are the bits? (I'm looking for information content,
you see.)
>
> > Basically, lose the instant email graffiti David, think first
then
> > think.
>
> My mote detector needle may have just twitched.
>
> > The LHS is always an integer, the RHS (Faulhaber formulae) is ..
the
> > RHS, call it n(a/b) if you want. But for sure it is not an
integer
> > all the time.
>
> Maybe the more classically educated here will remind me what school
of philosophy uses "for sure" as its basic underpinning.
>
> > That is the contradiction. Therefore the equality is
> > false,
>
> Hmmm, I've not got past the "for sure" bit yet  what part in which
syllogism does it play?
>
> > therefore it has no solution at any time.
>
> Woh! It looks like you're saying
>
> NOT(\forall a \in A f(a)=g(a))  \forall a \in A NOT(f(a)=f(b))
>
> I think you need to take your '' operator back to the store where
you bought it, and get your money back.
>
> > If you wish more light on the proof wrt to the Faulhaber
formulae,
> > then ask Donald Knuth. Phil, please tell me a good joke. Thank
you.
>
> Oooh, I may not have any letters afer my name (apart from the
courtesy 'Esq.'), but I _do_ have a $5.12 cheque from one Donald
Knuth, hand signed (with a felt tip pen by the looks of it!).
>
>
> Anyway, there was this large negative epsilon...
>
>
> Phil
>
>
> Don't be fooled, CRC Press are _not_ the good guys.
> They've taken Wolfram's money  _don't_ give them yours.
> http://mathworld.wolfram.com/erics_commentary.html
>
>
> Find the best deals on the web at AltaVista Shopping!
> http://www.shopping.altavista.com 0 Attachment
On Thu, 21 February 2002, "Michael Bell" wrote:> Surely it is whether you can make interesting contributions that matters.
[...]
> On that note, I'd like to announce the discovery of a record quadruplet:
Ooooh, nice. rho=210, rho^4=2G. Not a bad find at all.
>
> 10271674954.3000#+3461
> 10271674954.3000#+3463
> 10271674954.3000#+3467
> 10271674954.3000#+3469 (1284 digits)
Prefiltering would take that down to a 20M search space?
Hmmm, I know precisely how long that kind of search space takes to complete, he says tapping his fingers...
> proved prime by Primo, PRP tested using PFGW, sieved using APSieve. PRP
Snips are wonderful things.
> testing was done by the following people: Michael Bell, Michael Davison,
> Matt Jack, Ronald Lau, Graeme Leese and Benjamin Lowing.
>
> Sorry for the above noise,
> P.S. Chris: I don't seem to be able to submit these using the web entry
I may have been the cause of that! I went off and found what I thought was a record which looked like it was a reasonable margin larger than a previous one, but all I'd done is rediscover the record I was trying to beat, as all of margin of safety I'd given myself in the primorial had been composite. Not noticing this, I submitted, and Chris spotted the duplication manually, and I felt foolish. It's quite possible that primorials now are enforced as being of primes only. I'd certainly back that decision, if only to stop people as dim as me from tripping up where I did.
> form, is it because 3000 isn't prime?
Phil
Don't be fooled, CRC Press are _not_ the good guys.
They've taken Wolfram's money  _don't_ give them yours.
http://mathworld.wolfram.com/erics_commentary.html
Find the best deals on the web at AltaVista Shopping!
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At 01:27 AM 2/22/2002 0800, Paul Leyland wrote:
>Seeing that you raised the topic, let's see if anyone else here wants to
Did you two cash your checks? I kept mine, My wife thinks that I will be
>admit to having a Knuth check
in a very small minority of check recipients who didn't cash the check, I
think that most people will keep the check.
++
 Jud McCranie 
 
 Programming Achieved with Structure, Clarity, And Logic 
++
[Nontext portions of this message have been removed] 0 Attachment
> From: Jud McCranie [mailto:jud.mccranie@...]
to
> At 01:27 AM 2/22/2002 0800, Paul Leyland wrote:
>> Seeing that you raised the topic, let's see if anyone else here wants
>> admit to having a Knuth check
will
> Did you two cash your checks? I kept mine, My wife thinks that I
> be in a very small minority of check recipients who didn't cash the
check,
> I think that most people will keep the check.
Mine is framed and on my study wall at home. Next to framed repros of
my RSA129 and RSA140 checks. Still need to get the RSA155 check
done.
I'd heard that hardly anyone has ever cashed a Knuth check.
A check for $2.88 is actually quite worthless over here in the UK. A
bank charges far more than that to process it.
Paul 0 Attachment
On Fri, 22 February 2002, "Paul Leyland" wrote:> > Did you two cash your checks? I kept mine, My wife thinks that I
Some people just don't understand what gives things 'value'. Monetary aspects are relatively minor in that regard.
> will
> > be in a very small minority of check recipients who didn't cash the
> check,
I nearly jetisoned a #200 camera at while a the front of a Moody/Marsden/Ashton/Paice/Moore charity gig once, in order to catch one of Ian Paice's flying drumsticks! I was only a teenager at the time though. However, even today my Bathroom is 'papered' with setlists of people like Wishbone Ash, and basically any gig where it's possible to climb up on stage!
> > I think that most people will keep the check.
Not I, certainly. In fact I will go further  mine's not framed yet, but when I do frame it I will also include the handwritten notes on the printout of the email I sent him. That's how sad I am! Sad, but happy :)
>
> Mine is framed and on my study wall at home. Next to framed repros of
> my RSA129 and RSA140 checks. Still need to get the RSA155 check
> done.
>
> I'd heard that hardly anyone has ever cashed a Knuth check.
> A check for $2.88 is actually quite worthless over here in the UK. A
Here too. We're charged ~E20. I found this out after cashing a $13.80 check, and ending up _out of pocket_.
> bank charges far more than that to process it.
Phil  waaaaaay off topic, sorry.
It is against US Department of Agriculture regulations to
advertise or sell as "Prime Rib" any cut of meat containing a
nonprime number of ribs.
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At 08:31 AM 2/22/2002 0800, Paul Leyland wrote:
>Mine is framed and on my study wall at home.
I had mine out ($3.84), but it is faint, and I thought that the light may
be making it fade, so I put it in an envelope in the filing cabinet to keep
it out of the light.
>I'd heard that hardly anyone has ever cashed a Knuth check.
That's what I thought. Now if I get a $1,000 check from Erdos .....
++
 Jud McCranie 
 
 Programming Achieved with Structure, Clarity, And Logic 
++ 0 Attachment
At 09:09 AM 2/22/2002 0800, Phil Carmody wrote:
> Not I, certainly. In fact I will go further  mine's not framed yet, but
when I do frame it I will also include the handwritten notes on the
printout of the email I sent him.
Might better keep it out of sunlight. I'd sent two paper letters, and I
got the check (and my letters with handwritten notes) in the mail about 11
years later. I counted that I'd moved 5 times in the intervening period,
so he tracked me down somehow.
++
 Jud McCranie 
 
 Programming Achieved with Structure, Clarity, And Logic 
++ 0 Attachment
> But I have noticed
Perhaps the real DB does, but his alterego simply fails to.
> one thing, why does D Broadhurst pretend not to understand my
> namesake's contributions?
Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com 0 Attachment
I just joined the list a couple of days ago. So I just wanted to say hello to
everyone.
My name is Mark Hammond, I live in Tucson, Az.
I don't know if I'll have much to add to the discussions, though my background
is in math, but I'll try.
It looks like the list has interesting topics that will give me a chance to
exercise my mental muscles.
I found out about it, because I've long been interested in the Perfect Cuboid
problem, and while doing a search on it the other day, I saw to my amazement,
that someone (Jon Perry) claimed to have a proof that it couldn't be done. It
also nearly gave me a heart attack, because I've been organizing an internet
search for it.
After looking over the proof and rereading it several times, I spotted the
errors in it. So it's still an open question.
The search turned up a post to this list about the proof...which led to my
decision to join...to make a long story short.
It might be offtopic, but as I mentioned I'm organizing a computer search for
it and if anyone would like to help out, email me offlist for details.
Thanks. 0 Attachment
> From: Mark Hammond [mailto:markch1@...]
Perhaps this should be added to the prime mailing list FAQ ;)
> the Perfect Cuboid problem, and while doing a search on
> it the other day, I saw to my amazement,
> that someone (Jon Perry) claimed to have a proof that it
> couldn't be done...
>
> After looking over the proof and rereading it several times,
> I spotted the errors in it.
__________________________________________________
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There are a lot of consecutive lines without any primes, or primes*primes.
For example :
3000000000000000000000000000028 3000000000000000000000000000029
3000000000000000000000000000030
3000000000000000000000000000031 3000000000000000000000000000032
3000000000000000000000000000033
3000000000000000000000000000034 3000000000000000000000000000035
3000000000000000000000000000036
3000000000000000000000000000037 3000000000000000000000000000038
3000000000000000000000000000039
3000000000000000000000000000040 3000000000000000000000000000041
3000000000000000000000000000042
3000000000000000000000000000043 3000000000000000000000000000044
3000000000000000000000000000045
3000000000000000000000000000046 3000000000000000000000000000047
3000000000000000000000000000048
3000000000000000000000000000049 3000000000000000000000000000050
3000000000000000000000000000051
3000000000000000000000000000052 3000000000000000000000000000053
3000000000000000000000000000054
3000000000000000000000000000055 3000000000000000000000000000056
3000000000000000000000000000057
3000000000000000000000000000058 3000000000000000000000000000059
3000000000000000000000000000060
 Original Message 
From: "Jensen Lee" <jensenlee@...>
.
>
> I discovered a pattern in primes which i'm not sure if anyone has
> seen before, but it involves primes and prime*primes. It goes like
> this.
>
>
> 55 56 57 55 is p*p 5*11
> 52 53 54 53 is prime
> 49 50 51 49 is p*p 7*7 < 51 is also p*p
> 46 47 45 47 is prime
> 43 44 45 43 is prime
> 40 41 42 41 is prime
> 37 38 39 37 is prime
> 34 35 36 35 is p*p 7*5 < 34 is also p*p
> 31 32 33 31 is prime
> 28 29 30 29 is prime
> 25 26 27 25 is p*p 5*5
> 22 23 24 23 is prime
> 19 20 21 19 is prime
> 16 17 18 17 is prime
> 13 14 15 13 is prime
> 10 11 12 11 is prime
> 7 8 9 7 is prime
> 4 5 6 5 is prime
> 1 2 3 2 and 3 are prime, 1 is p*p
>
> ..... 0 Attachment
Jensen Lee wrote:
> I'm new to this group
Welcome to the group.
> I discovered a pattern in primes which i'm not sure if anyone has
You choose to skip all numbers divisible by 2 and 3. The zigzag pattern is
> seen before, but it involves primes and prime*primes. It goes like
> this.
>
>
> 55 56 57 55 is p*p 5*11
> 52 53 54 53 is prime
> 49 50 51 49 is p*p 7*7
> 46 47 45 47 is prime
> 43 44 45 43 is prime
> 40 41 42 41 is prime
> 37 38 39 37 is prime
> 34 35 36 35 is p*p 7*5
> 31 32 33 31 is prime
> 28 29 30 29 is prime
> 25 26 27 25 is p*p 5*5
> 22 23 24 23 is prime
> 19 20 21 19 is prime
> 16 17 18 17 is prime
> 13 14 15 13 is prime
> 10 11 12 11 is prime
> 7 8 9 7 is prime
> 4 5 6 5 is prime
> 1 2 3 2 and 3 are prime, 1 is p*p
>
> if you highlight the prime and prime*prime numbers in the first and
> second columns you can get a simple zigzag pattern. For some reason
> this doesn't include 2 and 3 as these are special case numbers.
exactly all other numbers. The smallest such number which is not a prime or
prime*prime (called semiprime) is clearly 5*5*5 = 125. Eventually almost all
numbers will have at least 3 prime factors  and at least n for any fixed n.
> if z is a p*p, then I have a few maths bits i came up with
Nothing to do with semiprimes.
>
> z = 6x + 1
2 divides 6x, 6x+2, 6x+4. 3 divides 6x+3. Then all numbers not divisible by 2
or 3 is on the form 6x +1.
> z = y + i*sqrt(y) (i = 0,2,4,6,8,...)
Nothing to do with semiprimes.
If y divides odd z then there is even i with:
z = y*(1+i) = y + i*y = y + i*sqrt(y^2).
> z = p1*p2
That was your assumption.
> I found that under 1000 there are 168 prime*prime
There are 168 primes under 1000. 169 if you include 1, but 1 is usually not
> and 169 primes. This seems to be some sort of balancing point.
considered prime by definition.
I don't know which numbers you counted to reach 168 prime*prime. There are 299
semiprimes below 1000. 204 of them are odd. 138 are both odd and not divisible
by 3.
Numbers with many factors start out rare. For all natural m,n with m<n, there
should be a balance point f(m,n) (or a set of points relatively close
together) where numbers with n factors become more common.
> Is this an old method coz I can't seem to find this in books.
Sorry, but it is mostly simple observations not interesting enough to put in
books. However, all numbers not divisible by 2 or 3 being on the form 6x + 1
is often mentioned. Many amateur mathematicians think they are the first to
discover this or a simple variant of it.

Jens Kruse Andersen 0 Attachment
Hello,
I do not know college level math (yet), but that does not stop me from studying and learning really cool things about primes. I am able to use paper,pen, and archimedian tesselated graph paper, to make diagrams dealing with primes.
I do not use GIMPS. I try to find primes on my own. My highest prime I have found and tested positive, is 4027 digits.
I hope to break that personal record, once a possible prime I am testing finishes.
It is a 2p1 Mersenne type prime. P being a prime that is 6 digits and starts with 9. I am sure it is well known here, the world record Mersenne prime, p is 6 digits and starts with 4.
I am guessing, if my number is positive, it would be about 26 million digits.
I tested my number with Mathematica 9 primality testing. It ran the number for 20 days before my computer crashed. That was using a platter HDD. Now I am running 3 OCZ Vertex 2 SSDs in raid 0, for extra speed,and upgraded from Windows 7 32 bit to 64 bit.
I have been rerunning the test for 3 days now on my main PC, but have also been running it on my laptop since January 19th, in case of another crash.
I have recently found the primality theorum, (2p+1)/3.
I started that on Mathematica 9 last night and tonight it is still running.
I work on primes with all of my spare time, apart from work. My 2 roommates think I am nuts, but I am having fun and found I really enjoy math.
I joined this group hoping to meet like minded people, and maybe get advice. I do not yet know how to use Mathematica's abilities.
I have made a graph by hand, that shows values of psquared, with symetrical high sine waves, and mirrored asymetrical low sine waves in between.I can explain that more, if anyone is interested.
Thanks,
Dwayne 0 Attachment
You might find interesting stuff to read on mersenneforum.org
(not limited to Mersenne primes),
which is a forum easier to navigate through than this group (I think).
Also, a better place for informal discussions,
getting help from friendly users,
and a little more on the "fun" side.
Maximilian
>
[Nontext portions of this message have been removed]
> I work on primes with all of my spare time, apart from work. My 2
> roommates think I am nuts, but I am having fun and found I really enjoy
> math.
> I joined this group hoping to meet like minded people, and maybe get
> advice. I do not yet know how to use Mathematica's abilities.
> (...)
> Thanks,
> Dwayne
>
 0 Attachment
On Mon, 20130128 at 22:36 0400, Maximilian Hasler wrote:>
Indeed. Be aware, though, that the forum owner and supermods (I'm one)
> You might find interesting stuff to read on mersenneforum.org
> (not limited to Mersenne primes),
> which is a forum easier to navigate through than this group (I think).
>
> Also, a better place for informal discussions,
> getting help from friendly users,
> and a little more on the "fun" side.
>
> Maximilian
have a rather idiosyncratic sense of humour and that some of the forum
behaviour isn't always what you might have expected. That said, it is a
very friendly and helpful site, by and large. I've learned a lot there
and have taught a lot there too.
Neither is it limited to primes, mersenne or otherwise. As well as the
obvious factorization threads, there are also discussions about science,
technology, mathematics, politics, finance, health and several versions
of general purpose silliness.
OK, adbreak over. We now return you to your scheduled programming.
Paul
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