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Mark Spahn

Joined: 07 Jul 2005
Posts: 62

Posted: Thu Jul 20, 2006 6:45 pm    Post subject: Re: D-numbers: a generalization of Sophie Germain twin primes

Hi Mori,

Thanks for cleaning up my garbled text; I made a change to it
to make it more readable ('plain text'), but it had the opposite effect.
I noticed later that the OP's website had a clearer definition
than his post: A prime p is a twin prime iff p+2 is also prime.
Thus, by the OP's definition, 41 is a twin prime but 43 is not.
This definition, even if non-standard, makes sense, given his
further remarks. A Sophie Germain (who dat?) prime is a
prime p for which 2p+1 is also a prime.
Thus a Sophie Germain twin prime is a prime p for which
both p+2 and 2p+1 are also primes.
For any prime p, if d>0 and d|p, then d=1 or p,
and the set {p+d+1 such that d>0 and d|p}
= {p+1+1, p+p+1} = {p+2, 2p+1},
and iff these two numbers are also prime,
then p is a Sophie Germain twin prime.

Mark Spahn

"moriman" <morimanNONO@NObtinternetNO.com> wrote in message news:R66dnUju1s4MXCLZRVnygQ@bt.com...
Hi Mark,

I'm top-posting as your html post is *nearly* unreadable :(

What you have said below is exactly what the OP posted, that twin-primes are
two primes of the form p & p+2.
You stated "By your (the OP's) definition, 3, 5, and 11 are twin primes, but
7, 13, and 19" where what the OP actually stated was "A twin prime is a
prime p such that p+2 is prime". Although I'll admit this is *slightly*
ambiguous, I'm sure that most readers would have got the exact meaning that
if p is a prime and p+2 is a prime then they are twin primes.

This continues to the Sophie Germain prime, where if p and 2p+1 are prime,
then p is called a Sophie Germain prime.
i.e. p=3 is a Sophie Germain prime because 2p+1 = 7 which is also prime. 7
is *not* a SG prime since p=7 gives 2p+1=15 which is not prime.

So, a quick reiteration: twin primes are a *pair* of numbers where p and p+2
are prime; a Sophie Germain prime is a *single* prime p, where p and 2p+1
are prime.

As for the OP's final "...arises as p+d+1 for all divisors d of p", I'm with
you on that one, since if p is prime then it doesn't have *any* divisors d
other than itself and unity.

hth

mori
Phil Carmody
science forum Guru Wannabe

Joined: 05 Jun 2005
Posts: 267

Posted: Thu Jul 20, 2006 6:45 am    Post subject: Re: D-numbers: a generalization of Sophie Germain twin primes

s.m.r. dropped - can't post to moderated groups.
f/u set to a.m.r.

"wkehowski@cox.net" <wkehowski@cox.net> writes:
 Quote: Hello, A twin prime is a prime p such that p+2 is prime and a Sophie Germain prime if 2p+1 is prime. Oberve that the pair p+2, 2p+1 as arises as p+d+1 for all divisors d of p. Thus, we have Definition. A positive integer satisfies Property D and is called a D-number if n+d+1 is prime for all divisors d of n. Let D be the set of all D-numbers. After watching a Maple program find and print the factored elements of this set to the screen one instantly observes that apparently the only integers that arise are 1, 9 (the only square), biprimes with two distinct factors, and triprimes of all possible types: p^3, p^2*q, and p*q*r. The first prime r such that 3*3*r is in D is r=370884, while the first prime r such that 3*7*r is in D is r=606619339. If you're interested, there are text files and conjectures here: http://glory.gc.maricopa.edu/~wkehowsk/propertyd/index.html

No further squares.
Look at the >=9 values modulo 3.
(you only need to look at the +1+1 and +3+1 values)

Phil
--
The man who is always worrying about whether or not his soul would be
damned generally has a soul that isn't worth a damn.
-- Oliver Wendell Holmes, Sr. (1809-1894), American physician and writer

and this bizarre comment is purely inserted so that I can google directly
to this thread later, in case I have a tedious and tawdry day at work...
ungernerik@aol.com
science forum beginner

Joined: 11 May 2006
Posts: 11

Posted: Sat Jul 15, 2006 2:02 am    Post subject: Re: Loose connectivity, factoring and residues

jstevh@msn.com wrote:
 Quote: jstevh@msn.com wrote: The factoring problem can be easily approached using simple algebra. Start with x^2 - y^2 = S - 2*x*k where all are integers, as notice then you trivially have x^2 + 2*x*k + k^2 = y^2 + S + k^2 so x+k = sqrt(y^2 + S + k^2) and finding y is just a matter of factoring (S+k^2)/4. Now with just the explicit equation you end up with nothing but trivialities, but turning to congruences, you can now simply let x^2 - y^2 = 0 mod T which--this is important--now forces S - 2*x_res*k = 0 mod T where I put in x_res to emphasize that now it's congruences, so there is loose connectivity and an explicit value of x is not needed--just a residue. But now I can just solve for k, assuming 2, S and x are coprime to T: k = S*(2*x_res)^{-1} mod T where (2*x_res)^{-1} is the modular inverse of (2*x_res) mod T. One thing that has come up in this thread in my discussion with Tim Peters is that the mathematics will solve for any T that has the k and S given, so you have the possibility that when you solve out for x and y, you find that x^2 - y^2 is coprime to YOUR target T, because the mathematics has solved for another that fits with those same equations with a different x_res.. However that seems to occur mostly with relatively large y, so minimizing y, is a practical result of that analysis, which is why theory does not necessarily mean you immediately have a practical solution. I like the analogy of the atomic bomb. Posters pestering me to immediately solve an RSA Challenge number are like if people had pestered Einstein to explode a nuclear bomb before they'd consider his theories. That the modular inverse makes an appearance is critical, but more importantly I now have a way to find all the variables!!! That can be done by simply picking a residue for x_res and then picking S, like x_res = 1, and S =1, to get k. For instance if T=35, and I use x_res=S=1, then k = 18 mod 35, and k=18 will suffice. Then y is found by factoring (1+18^2)/4 and then you have x as well. Using the identity: (f_1 + f_2)^2 = (f_1 - f_2)^2 + 4*f_1*f_2 Of course there will exist and x and y such that x^2 - y^2 = 0 mod T for any x_res you choose, which is trivial to prove, as that is equivalent to x^2 - y^2 = kT where k can be any integer. And that remains true. Clearly now one issue is to find a relatively small y, as in the examples that Tim Peters emphasized, y was so much larger than x, that x^2 - y^2 was negative. So an equation that is useless explicitly becomes quite powerful with modular algebra--introducing loose connectivity--leading to a general method for factoring. And remember, part of my point with these ideas is that supposedly "pure" mathematicians CAN ignore exciting and interesting research--for political reasons--as these people are just liars. They may know I have other major mathematical finds, where I couldn't force the issue like with the factoring problem, where these twisted people chose to sit quietly, or in some cases, claim my research was wrong, like those sci.math people who petitioned the math journal that published a paper of mine, and the paper got yanked, and later the damn math journal died! The proof here for those of you willing to accept it, is in the simple mathematics, STILL being ignored by the mainstream mathematical community to my knowledge, as they are corrupt, and don't actually give a damn about mathematics, seeing it only as a political and economic tool for their own benefit. James Harris

You've got:

x^2 - y^2 = kT

where k can be any integer.

and:

Clearly now one issue is to find a relatively small y...

For small y, try the following for k, in the order listed:

1, 3, 4, 12, 5, 15, 24, 20, 8, 40, 21, 7, 35, 45, 60, ...
science forum beginner

Joined: 05 Jun 2005
Posts: 13

Posted: Tue Jul 04, 2006 7:02 pm    Post subject: Re: The Speed of Toilet Paper

barbara@bookpro.com wrote in
news:a49la2dhposngbp4u3o9nh9j3edm5t3mbd@4ax.com:

 Quote: On 4 Jul 2006 03:16:08 GMT, "TeaLady (Mari C.)" spressobean@yahoo.com> wrote: Rich Holmes wrote in news:u44py7s06s.fsf@mep1.phy.syr.edu: "David Moran" writes: "William Elliot" wrote in message news:Pine.BSI.4.58.0606261857001.7321@vista.hevanet.com.. . On Tue, 27 Jun 2006, Jeff wrote: Here's the kind of things you can do to have some fun with math: Americans use enough toilet paper in one day to wrap around the world nine times. Do the math, it's physically impossible. In round numbers Earth's diameter is 13000 km; its circumference is 40000 km or 4E7 m. Population of the US is roughly 300 million. 9 x 4E7 m / 3E8 = 3 x 4E-1 = 1.2 meters per person per day. That's the right order of magnitude. More is actually used - ever watch a toddler get ready to wipe its butt ? Takes 1/2 a roll just to find the right piece, and then it is dropped, declared dirty, and the wearch starts all over again. Stop spying on Lots42! Or at least don't tell us anything further about what he does in the bathroom.

I think he secretly teaches 3 year olds how to doidy in his
spare time (which seems to be almost always). No need to spy
on him anyhow - he 'fesses all to all when the mood strikes.

--

"The principle of Race is meant to embody and express the
utter negation of human freedom, the denial of equal rights, a
challenge in the face of mankind." A. Kolnai
Avast ye scurvy dogs ! Thar be no disease in this message.
science forum beginner

Joined: 05 Jun 2005
Posts: 13

Posted: Tue Jul 04, 2006 6:50 pm    Post subject: Re: The Speed of Toilet Paper

John D Salt <jdsalt_AT_gotadsl.co.uk> wrote in

 Quote: "TeaLady (Mari C.)" wrote in news:Xns97F5ECB5A640Dspblt@130.133.1.4: [Snips] More is actually used - ever watch a toddler get ready to wipe its butt ? Takes 1/2 a roll just to find the right piece, and then it is dropped, declared dirty, and the wearch starts all over again. I don't know if it's safe to ask what a "wearch" is. Do we have them in Wales? All the best, John.

Weary search, I guess.

Or a t ypo.

--

"The principle of Race is meant to embody and express the utter
negation of human freedom, the denial of equal rights, a
challenge in the face of mankind." A. Kolnai
Avast ye scurvy dogs ! Thar be no disease in this message.
barbara@bookpro.com
science forum beginner

Joined: 12 Jan 2006
Posts: 22

Posted: Tue Jul 04, 2006 5:25 pm    Post subject: Re: The Speed of Toilet Paper

On 4 Jul 2006 03:16:08 GMT, "TeaLady (Mari C.)"
<spressobean@yahoo.com> wrote:

 Quote: Rich Holmes wrote in news:u44py7s06s.fsf@mep1.phy.syr.edu: "David Moran" writes: "William Elliot" wrote in message news:Pine.BSI.4.58.0606261857001.7321@vista.hevanet.com... On Tue, 27 Jun 2006, Jeff wrote: Here's the kind of things you can do to have some fun with math: Americans use enough toilet paper in one day to wrap around the world nine times. Do the math, it's physically impossible. In round numbers Earth's diameter is 13000 km; its circumference is 40000 km or 4E7 m. Population of the US is roughly 300 million. 9 x 4E7 m / 3E8 = 3 x 4E-1 = 1.2 meters per person per day. That's the right order of magnitude. More is actually used - ever watch a toddler get ready to wipe its butt ? Takes 1/2 a roll just to find the right piece, and then it is dropped, declared dirty, and the wearch starts all over again.

Stop spying on Lots42! Or at least don't tell us anything further
about what he does in the bathroom.

BW
John D Salt
science forum beginner

Joined: 15 Jun 2005
Posts: 3

Posted: Tue Jul 04, 2006 9:45 am    Post subject: Re: The Speed of Toilet Paper

"TeaLady (Mari C.)" <spressobean@yahoo.com> wrote in
news:Xns97F5ECB5A640Dspblt@130.133.1.4:

[Snips]
 Quote: More is actually used - ever watch a toddler get ready to wipe its butt ? Takes 1/2 a roll just to find the right piece, and then it is dropped, declared dirty, and the wearch starts all over again.

I don't know if it's safe to ask what a "wearch" is. Do we have them in
Wales?

All the best,

John.
science forum beginner

Joined: 05 Jun 2005
Posts: 13

Posted: Tue Jul 04, 2006 3:20 am    Post subject: Re: The Speed of Toilet Paper

Chris McGonnell <smeagol@NOkey-net.net> wrote in
news:3pb5a2lrtfok1ut655pcjes2m3ot1kv76a@4ax.com:

 Quote: On Wed, 28 Jun 2006 09:21:03 -0600, Kevin S. Wilson wrote: On Tue, 27 Jun 2006 20:56:01 -0700, William Elliot marsh@hevanet.remove.com> wrote: snip "shucks" an exclamation of mild disappointment, disgust, etc. He thinks "shucks" is a big word? That's kinda sad, innit? Well, Billy's busy with his dance classes and his working class family over there in UKasia, so I suppose "shucks" *is* an awfully big word to him. I mean, I imagine British dance schools don't emphasize literacy, do you?

What if he is a she, and lack of endowment down there is a
preferable thing ?

Eh ?

--

"The principle of Race is meant to embody and express the utter
negation of human freedom, the denial of equal rights, a
challenge in the face of mankind." A. Kolnai
Avast ye scurvy dogs ! Thar be no disease in this message.
science forum beginner

Joined: 05 Jun 2005
Posts: 13

Posted: Tue Jul 04, 2006 3:16 am    Post subject: Re: The Speed of Toilet Paper

Rich Holmes<rsholmes+usenet@mailbox.syr.edu> wrote in
news:u44py7s06s.fsf@mep1.phy.syr.edu:

 Quote: "David Moran" writes: "William Elliot" wrote in message news:Pine.BSI.4.58.0606261857001.7321@vista.hevanet.com... On Tue, 27 Jun 2006, Jeff wrote: Here's the kind of things you can do to have some fun with math: Americans use enough toilet paper in one day to wrap around the world nine times. Do the math, it's physically impossible. In round numbers Earth's diameter is 13000 km; its circumference is 40000 km or 4E7 m. Population of the US is roughly 300 million. 9 x 4E7 m / 3E8 = 3 x 4E-1 = 1.2 meters per person per day. That's the right order of magnitude.

More is actually used - ever watch a toddler get ready to wipe
its butt ? Takes 1/2 a roll just to find the right piece, and
then it is dropped, declared dirty, and the wearch starts all
over again.

--

"The principle of Race is meant to embody and express the
utter negation of human freedom, the denial of equal rights, a
challenge in the face of mankind." A. Kolnai
Avast ye scurvy dogs ! Thar be no disease in this message.
William Elliot
science forum Guru

Joined: 24 Mar 2005
Posts: 1906

Posted: Sat Jul 01, 2006 2:16 am    Post subject: Re: The Speed of Toilet Paper

On Fri, 30 Jun 2006, Adam Funk wrote:
 Quote: HAWYAW If you're going to try to be patronizing, do it right. You're right, he should have started with HEEHAW. Hello extraneous extras hiding awesome warps.
science forum beginner

Joined: 07 Jun 2005
Posts: 37

Posted: Fri Jun 30, 2006 8:11 pm    Post subject: Re: The Speed of Toilet Paper

On 2006-06-30, barbara@bookpro.com <barbara@bookpro.com> wrote:

 Quote: "William Elliot" wrote in message HAWYAW If you're going to try to be patronizing, do it right.

You're right, he should have started with HEEHAW.

--
Vielen Dank
David DeLaney
science forum beginner

Joined: 08 May 2005
Posts: 20

Posted: Fri Jun 30, 2006 1:47 pm    Post subject: Re: The Speed of Toilet Paper

moriman <moriman-spamless@btinternet.com> wrote:
 Quote: "William Elliot" wrote in message news:Pine.BSI.4.58.0606290445370.7950@vista.hevanet.com... On Thu, 29 Jun 2006, Adam Funk wrote: On 2006-06-29, William Elliot wrote: Around here "I" am a very big word. IFYPFY. HAWYAW Around here "I" am a very big word => Around here "I am" is a very big word

No no no. "Around here 'I' be a very big word, yo you!"

Dave
--
\/David DeLaney posting from dbd@vic.com "It's not the pot that grows the flower
It's not the clock that slows the hour The definition's plain for anyone to see
Love is all it takes to make a family" - R&P. VISUALIZE HAPPYNET VRbeable<BLINK>
http://www.vic.com/~dbd/ - net.legends FAQ & Magic / I WUV you in all CAPS! --K.
barbara@bookpro.com
science forum beginner

Joined: 12 Jan 2006
Posts: 22

Posted: Fri Jun 30, 2006 11:23 am    Post subject: Re: The Speed of Toilet Paper

On Fri, 30 Jun 2006 02:20:43 -0700, William Elliot
<marsh@hevanet.remove.com> wrote:

 Quote: On Fri, 30 Jun 2006, moriman wrote: "William Elliot" wrote in message On Thu, 29 Jun 2006, Adam Funk wrote: On 2006-06-29, William Elliot wrote: Around here "I" am a very big word. IFYPFY. HAWYAW Around here "I" am a very big word => Around here "I am" is a very big word Bushits, you guys are unbelievable. Amongst you, even 'a' is a big word. Y'all always be talking in big words.

If you're going to try to be patronizing, do it right.

BW
William Elliot
science forum Guru

Joined: 24 Mar 2005
Posts: 1906

Posted: Fri Jun 30, 2006 9:20 am    Post subject: Re: The Speed of Toilet Paper

On Fri, 30 Jun 2006, moriman wrote:
 Quote: "William Elliot" wrote in message On Thu, 29 Jun 2006, Adam Funk wrote: On 2006-06-29, William Elliot wrote: Around here "I" am a very big word. IFYPFY. HAWYAW Around here "I" am a very big word => Around here "I am" is a very big word Bushits, you guys are unbelievable.

Amongst you, even 'a' is a big word.
Y'all always be talking in big words.
moriman
science forum beginner

Joined: 06 Apr 2006
Posts: 26

Posted: Fri Jun 30, 2006 8:06 am    Post subject: Re: The Speed of Toilet Paper

"William Elliot" <marsh@hevanet.remove.com> wrote in message
news:Pine.BSI.4.58.0606290445370.7950@vista.hevanet.com...
 Quote: On Thu, 29 Jun 2006, Adam Funk wrote: On 2006-06-29, William Elliot wrote: Around here "I" am a very big word. IFYPFY. HAWYAW

Around here "I" am a very big word => Around here "I am" is a very big word

mori

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