## Twin Primes

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• Hi, similar to the reisel and the Sierpinski problem is there a twin prime conjecture for k such that k is a multiple of 3 and k*2^n+1 | k*2^n-1 can never be
Message 1 of 17 , Jul 18, 2003
Hi,
similar to the reisel and the Sierpinski problem is there a twin
prime conjecture for k such that k is a multiple of 3 and

k*2^n+1 | k*2^n-1 can never be prime for sure.(ie. one of then always
has a factor)

I have found twin primes for all numbers less than 3*37=111.

Thanks!
Harsh Aggarwal
• Brier Numbers are values of k that are simultaneously Reisel numbers and Sierpinski Numbers. Several Brier numbers are known. These would clearly be
Message 2 of 17 , Jul 18, 2003
Brier Numbers are values of "k" that are simultaneously Reisel numbers
and Sierpinski Numbers. Several Brier numbers are known. These would
clearly be examples of "no twin primes" because there would be no
primes on either side.

--- In primenumbers@yahoogroups.com, "eharsh82" <harsh@u...> wrote:
> Hi,
> similar to the reisel and the Sierpinski problem is there a twin
> prime conjecture for k such that k is a multiple of 3 and
>
> k*2^n+1 | k*2^n-1 can never be prime for sure.(ie. one of then always
> has a factor)
>
> I have found twin primes for all numbers less than 3*37=111.
>
> Thanks!
> Harsh Aggarwal
• ... As I posted here last November: http://groups.yahoo.com/group/primenumbers/message/9844 The value k=111 almost certainly yields no twins of the form
Message 3 of 17 , Jul 18, 2003
Harsh wrote:
> similar to the reisel and the Sierpinski problem is there a twin
> prime conjecture for k such that k is a multiple of 3 and
>
> k*2^n+1 | k*2^n-1 can never be prime for sure.(ie. one of then always
> has a factor)
>
> I have found twin primes for all numbers less than 3*37=111.

As I posted here last November:

The value k=111 almost certainly yields no twins of the form k*2^n+/-1.

Proving it seems unlikely.
• To your knowledge, is there any online list of the first thousand or so sets of twin primes? [Non-text portions of this message have been removed]
Message 4 of 17 , Feb 13, 2004
To your knowledge, is there any online list of the first thousand or so sets of twin primes?

[Non-text portions of this message have been removed]
• type twin prime list into google and click on the second link. sibley
Message 5 of 17 , Feb 13, 2004
type "twin prime list" into google and click on the second link.

sibley

On Feb 13, 2004, at 2:46 PM, Marty Weissman wrote:

> To your knowledge, is there any online list of the first thousand or
> so sets of twin primes?
>
>
> [Non-text portions of this message have been removed]
>
>
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
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• Thanks to all for the help.
Message 6 of 17 , Feb 13, 2004
Thanks to all for the help.
• My real proof of the infinitude of twin primes url had a period at the end because of the sentence it was in, here it is, it should go through this time:
Message 7 of 17 , Jun 10, 2004
My real proof of the infinitude of twin primes url had a period
at the end because of the sentence it was in, here it is, it
should go through this time:

http://www.lulu.com/bsmath
• Hi, While I am amazed at the impressive progress made with twin primes, I cannot help feeling some of the basic prime questions for e.g. as to why twin primes
Message 8 of 17 , Nov 7, 2004
Hi,
While I am amazed at the impressive progress made with
twin primes, I cannot help feeling some of the basic
prime questions for e.g. as to why twin primes appear
only in certain positions in prime sequence and not in
other positions remain unanswered (to my knowledge).

However much we may pursue with impressive advances in
primes, the fact remains prime structure basics will
have to be understood to provide the solid foundation
for all the impressive advances in primes.

I wish to submit my submission on prime structures
carries answers to some of these basic questions and
look forward to building stronger foundations of prime
behaviour based on prime structures.

L.J.Balasundaram

__________________________________
Do you Yahoo!?
Check out the new Yahoo! Front Page.
www.yahoo.com
• As far as the twin primes we know, is it true that there is a pair between every set of integers between P and P squared, where P is any prime number 2?
Message 9 of 17 , Apr 24, 2005
As far as the twin primes we know, is it true that there is a pair between every set of integers between P and P squared, where P is any prime number > 2?

[Non-text portions of this message have been removed]
• ... No, try 19. ? forprime(p=19^2,20^2,print(p)) 367 373 379 383 389 397 There s also 53. ? forprime(p=53^2,54^2,print(p)) 2819 2833 2837 2843 2851 2857 2861
Message 10 of 17 , Apr 24, 2005
On Sunday 24 April 2005 22:54, you wrote:
> As far as the twin primes we know, is it true that there is a pair between
> every set of integers between P and P squared, where P is any prime number
> > 2?

No, try 19.

? forprime(p=19^2,20^2,print(p))
367
373
379
383
389
397

There's also 53.

? forprime(p=53^2,54^2,print(p))
2819
2833
2837
2843
2851
2857
2861
2879
2887
2897
2903
2909

Nothing else up to 50000, and no other counterexamples are expected. That's
because heuristically, twin prime pairs in the vicinity of n occur about
every O(log^2 n) integers, and your interval has (n+1)^2 - n^2 = 2n + 1
integers. Since 2n + 1 grows faster than log^2 n, one would expect no
counterexamples to your statement other than these `small' ones. By the way,
numerical evidence using some better approximations (including constants and
so on) lends credence to this heuristic.

Décio

[Non-text portions of this message have been removed]
• ... You seem to modestly only ask for a twin prime pair between P and P^2. That is satisfied for all numbers 2
Message 11 of 17 , Apr 25, 2005
Marty Weissman wrote:

> As far as the twin primes we know, is it true that there is a pair between
> every set of integers between P and P squared, where P is any prime
> number > 2?

You seem to modestly only ask for a twin prime pair between P and P^2.
That is satisfied for all numbers 2 < P < 33218925*2^169690-1

33218925*2^169690+/-1 with 51090 digits is the largest known twin, found by
Danial Papp with Proth.exe.
For all smaller twins n+/-1, there is a known twin between this and (n-1)^2.

--
Jens Kruse Andersen
• Thanks to all who replied. ... From: Jens Kruse Andersen To: Sent: Monday, April 25, 2005 7:12 AM
Message 12 of 17 , Apr 25, 2005
Thanks to all who replied.
----- Original Message -----
From: "Jens Kruse Andersen" <jens.k.a@...>
Sent: Monday, April 25, 2005 7:12 AM

>
> Marty Weissman wrote:
>
>> As far as the twin primes we know, is it true that there is a pair
>> between
>> every set of integers between P and P squared, where P is any prime
>> number > 2?
>
> You seem to modestly only ask for a twin prime pair between P and P^2.
> That is satisfied for all numbers 2 < P < 33218925*2^169690-1
>
> 33218925*2^169690+/-1 with 51090 digits is the largest known twin, found
> by
> Danial Papp with Proth.exe.
> For all smaller twins n+/-1, there is a known twin between this and
> (n-1)^2.
>
> --
> Jens Kruse Andersen
>
>
>
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
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>
• I was trying to discover what I thought should be a simple thing, about primes the other day. Is there a way of calculating, for any PI(x) (within reason),
Message 13 of 17 , Jan 7, 2008
I was trying to discover what I thought should be a simple thing, about primes the other day.

Is there a way of calculating, for any PI(x) (within reason), what proportion in percentage terms the twin primes play their part?

Example: when (x) = 100, the twin primes account for 66.67% of the total primes.

Of course, in this example 5 has to be counted twice, - a condition not to be repeated later.

As PI(x) gets larger does the percentage of twin primes continue to decline in relation to the total primes, or does it settle down to a constant percentage? Are there any tables available and if so up to what value of PI(x)?

Many thanks

Bob

[Non-text portions of this message have been removed]
• ... http://www.ieeta.pt/~tos/primes.html Best, Andrey [Non-text portions of this message have been removed]
Message 14 of 17 , Jan 7, 2008
> Are there any tables available and if so up to what value of PI(x)?

http://www.ieeta.pt/~tos/primes.html

Best,

Andrey

[Non-text portions of this message have been removed]
• ... about primes the other day. ... proportion in percentage terms the twin primes play their part? ... total primes. ... not to be repeated later. ... decline
Message 15 of 17 , Jan 10, 2008
--- In primenumbers@yahoogroups.com, Bob Gilson <bobgillson@...>
wrote:
>
> I was trying to discover what I thought should be a simple thing,
>
> Is there a way of calculating, for any PI(x) (within reason), what
proportion in percentage terms the twin primes play their part?
>
> Example: when (x) = 100, the twin primes account for 66.67% of the
total primes.
>
> Of course, in this example 5 has to be counted twice, - a condition
not to be repeated later.
>
> As PI(x) gets larger does the percentage of twin primes continue to
decline in relation to the total primes, or does it settle down to a
constant percentage? Are there any tables available and if so up to
what value of PI(x)?
>
> Many thanks
>
> Bob
>
> [Non-text portions of this message have been removed]
>

Hi Bob,

The approximate number of primes <=x is pi(x) ~ x/log x.
The approximate number of twins <=x is pi2(x) ~ x/(log x)².
The quotient of both is log x.

WDS
• ## between 3 and 3*5; 3 pairs of twin primes; Prime number theorem estimates 0 ## between 3*5 and 3*5*7; 6 pairs of twin primes; Prime number theorem
Message 16 of 17 , Jul 19, 2011
## between 3 and 3*5; 3 pairs of twin primes;
Prime number theorem estimates 0

## between 3*5 and 3*5*7; 6 pairs of twin primes;
Prime number theorem estimates 5

## between 3*5*7 and 3*5*7*11; 32 pairs of twin primes;
Prime number theorem estimates 18

## between 3*5*7*11 and 3*5*7*11*13; 231 pairs of twin primes;
Prime number theorem estimates 144

## between 3*5*7*11*13 and 3*5*7*11*13*17; 2355 pairs of twin primes;
Prime number theorem estimates 1503

## between 3*5*7*11*13*17 and 3*5*7*11*13*19; 28999 pairs of twin primes;
Prime number theorem estimates 18961

## between 3*5*7*11*13*19 and 3*5*7*11*13*19*23; Estimated is :
Prime number theorem estimates 305907

For the prime number theorem estimates,
I used the formula

Upper/ ( (ln(upper))**2 - Lower/ ( (ln(lower))**2

I note that the estimates, estimated in this way are significantly lower
than actual.

I presume that someone has figured out a much better formula, still
consistent with the prime number theorem,
for estimating the number of twin primes less than a given integer.

Kermit
• ... http://primes.utm.edu/top20/page.php?id=1
Message 17 of 17 , Jul 19, 2011
> I presume that someone has figured out a much better formula, still
> consistent with the prime number theorem,
> for estimating the number of twin primes less than a given integer.

http://primes.utm.edu/top20/page.php?id=1
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