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Old 2018-03-14, 20:22   #144
Cybertronic
 
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For k-tuplets look also here
http://matheplanet.com/matheplanet/n...php?forum=9015
at page 1
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Old 2018-07-30, 19:00   #145
danaj
 
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Two Algorithms to Find Primes in Patterns

It isn't clear how efficient their code is for tuplets compared to mine. They ran with 150 cores and parallelize in the inner loop. I ran with 4 cores and parallelize at the outermost level for braindead simplicity (e.g. the sieve is serial but I run N ranges at a time). Extrapolating the time on my 4-thread Macbook to range and cores comes out to nearly the same time as they report, but that's a lot of extrapolation.

Their wheel is significantly larger than mine. I restrict mine based on space and to some extent speed (larger is not always faster, but it really depends on many factors including the depth and speed of primality testing, where I suspect my testing is faster than theirs).

My code just does clusters of {p,p+A,p+B,p+C,...} for any user entered A,B,C,.... Theirs also does things like {p,Ap+A',Bp+B',...} so they can look for Cunningham chains.
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Old 2018-07-31, 23:11   #146
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Quote:
Originally Posted by MattcAnderson View Post
Attached are probably my last efforts on prime constellation mathematics.

Please try to do a little bit more math,


the polynomial f(n)=n²+n+41 has the discriminant b²-4ac=-163 if you consider f(n)=an²+bn+c,
therefore you could also use the polynomial f(n)=n²+163 with the same discriminant
all primes with p|f(n) "appear" double periodically and can be sieved out by division.


If you are looking for some other quadratic polynomial my website may help you, especially http://devalco.de/poly_sec.php and

for the special polynomial f(n)=n²+163

http://devalco.de/basic_polynomials/...?a=1&b=0&c=163


I hope you will find some new ideas.


Greetings from the quadratic polynomials
Bernhard
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Old 2021-03-12, 09:13   #147
MattcAnderson
 
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"Matthew Anderson"
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https://sites.google.com/site/primeconstellations/

March 15 2022 - free Google site for PrimeConstellations has been deleted

Last fiddled with by MattcAnderson on 2022-03-16 at 04:00 Reason: dead link
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Old 2021-05-23, 14:38   #148
MattcAnderson
 
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Hi again all

see below

Prime Constellations of length eight


Search for Prime Constellations
Prime Constellations are more constant than the stars in the sky.

Even after the closest stars burn out and become dark, mathematical structure will exist. For example 1+1=2 is a timeless mathematical truth. This fact will always be so.

Look at this link about Goldbach's Comet.

Also interesting Tao-Green Theorem

March 2021

by Matt C. Anderson
email: matt.c1.anderson@gmail.com


A022011 Initial member of prime 8-tuplet (0,2,6,8,12,18,20,26) enumeration count 10,000 author WR
A022012 Initial member of prime 8-tuplet (0,2,6,12,14,20,24,26) enumeration count 10,000 author WR
A022013 Initial member of prime 8-tuplet (0,6,8,14,18,20,24,26) enumeration count 10,000 author WR
A022545 Initial member of prime 9-tuplet (0,2,6,8,12,18,20,26,30) enumeration count 10,000 author WR


8 (0,2,6,8,12,18,20,26) 11+210*n

8 (0,6,12,14,20,24,26) 17+30*n
8 (0,6,8,14,18,20,24,26) 173+210*n
9 (0,2,6,8,12,18,20,26,30) 11+210*n
9 (0,2,6,12,14,20,24,26,30) 17+30*n
9 (0,4,6,10,16,18,24,28,30) 13+30*n

Theses correct data took considerable effort.

Authors -
N.J.A. Slone = NJAS
Warut Roonguthai = WR
Matt C. Anderson = MCA
Tim Johannes Ohrtmann = TJO



To reiterate

A022011 Initial member of prime 8-tuplet (0,2,6,8,12,18,20,26) enumeration count 10,000 author WR
A022012 Initial member of prime 8-tuplet (0,2,6,12,14,20,24,26) enumeration count 10,000 author WR
A022013 Initial member of prime 8-tuplet (0,6,8,14,18,20,24,26) enumeration count 10,000 author WR
A022545 Initial member of prime 9-tuplet (0,2,6,8,12,18,20,26,30) enumeration count 10,000 author WR


That is a good place to stop for now.

matt.c1.anderson@gmail.com
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Old 2021-05-23, 14:40   #149
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forgot to add a webpage

https://sites.google.com/site/primeconstellations/

Matt
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Old 2021-09-07, 02:34   #150
MattcAnderson
 
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Default prime constellations web page

The attached file was hosted online by Google. Google provided this service to me for free.
Unfortunately, I am no longer able to edit the online file, and I don't know how long it will
be before it is wiped off the internet.

I want to share this information with the world.

There are many hours of original prime constellation calculations in this project.

Also, other people have done calculations, and the results are shared at The Online Encyclopedia of
Integer Sequences.org.

Have a look.

Matthew C. Anderson
Attached Files
File Type: pdf Search for Prime Constellations.pdf (215.5 KB, 77 views)
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Old 2021-09-07, 03:02   #151
chalsall
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Quote:
Originally Posted by MattcAnderson View Post
Have a look.
On every whiteboard I encounter I write \sqrt{-1}^2=? in the upper right-hand corner.

Very few find it funny. Which is exactly the point.
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Old 2021-10-18, 18:38   #152
MattcAnderson
 
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Hi all,

I found a webpage with a nice definition of Prime constellations. Especially I like that they specified no repetitions and some prime numbers can be skipped if it is a prime cluster.

Prime constellations are prime clusters with certain restrictions.

https://oeis.org/wiki/Prime_constellations

Regards,
Matt
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Old 2021-10-18, 20:46   #153
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Looks like a fun way to get into primes - it's something that would have aroused my interest a decade ago. But am I overlooking something? All these(the ones in the PDF) would take up to a second to find.

Last fiddled with by kuratkull on 2021-10-18 at 20:46 Reason: pdf
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Old 2021-10-19, 02:33   #154
MattcAnderson
 
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Quote:
Originally Posted by kuratkull View Post
Looks like a fun way to get into primes - it's something that would have aroused my interest a decade ago. But am I overlooking something? All these(the ones in the PDF) would take up to a second to find.
Hi all, Thank you for your interest Kuratkull.

Most of the prime lists I found were at least an overnight calculation.

I used the isprime() function in Maple and it is quite slow. But easy to use. I only learned 3 computer languages - Pascal, Maple, and HTML. I spent over two months of computer calculation back in 2006 to come up with some original calculations of shortest prime constellations. Lets look at the 9-tuples - in the OEIS.org/A022546. These are linked from "Search for Prime Constellations.pdf" file in this thread.

I did 200 prime number entries in the sequence. Then Dana Jacobsen did 800 more, taking the list to 1,000.

Now Normah Luhn has taken the lists even further and is actively working on it in 2021.
see http://www.pzktupel.de/ktuplets.htm
check line 27. List of the smallest prime k-tuplets.

Cheers
Matt

Last fiddled with by MattcAnderson on 2021-10-19 at 02:34 Reason: mispelled name
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