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 2018-03-14, 20:22 #144 Cybertronic     Jan 2007 Germany 2·239 Posts For k-tuplets look also here http://matheplanet.com/matheplanet/n...php?forum=9015 at page 1
 2018-07-30, 19:00 #145 danaj   "Dana Jacobsen" Feb 2011 Bangkok, TH 16158 Posts 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.
2018-07-31, 23:11   #146
bhelmes

Mar 2016

397 Posts

Quote:
 Originally Posted by MattcAnderson 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.

Bernhard

 2021-03-12, 09:13 #147 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 3·367 Posts 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
 2021-05-23, 14:38 #148 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 3×367 Posts 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
 2021-05-23, 14:40 #149 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 3×367 Posts forgot to add a webpage https://sites.google.com/site/primeconstellations/ Matt
2021-09-07, 02:34   #150
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

3×367 Posts
prime constellations web page

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.

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
 Search for Prime Constellations.pdf (215.5 KB, 77 views)

2021-09-07, 03:02   #151
chalsall
If I May

"Chris Halsall"
Sep 2002

101000110100112 Posts

Quote:
 Originally Posted by MattcAnderson 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.

 2021-10-18, 18:38 #152 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 21158 Posts 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
 2021-10-18, 20:46 #153 kuratkull     Mar 2007 Estonia 149 Posts 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
2021-10-19, 02:33   #154
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

3·367 Posts

Quote:
 Originally Posted by kuratkull 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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