20180314, 20:22  #144 
Jan 2007
Germany
2·239 Posts 

20180730, 19:00  #145 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
1615_{8} 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 4thread 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. 
20180731, 23:11  #146  
Mar 2016
397 Posts 
Quote:
Please try to do a little bit more math, the polynomial f(n)=n²+n+41 has the discriminant b²4ac=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 pf(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 

20210312, 09:13  #147 
"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 20220316 at 04:00 Reason: dead link 
20210523, 14:38  #148 
"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 TaoGreen Theorem March 2021 by Matt C. Anderson email: matt.c1.anderson@gmail.com A022011 Initial member of prime 8tuplet (0,2,6,8,12,18,20,26) enumeration count 10,000 author WR A022012 Initial member of prime 8tuplet (0,2,6,12,14,20,24,26) enumeration count 10,000 author WR A022013 Initial member of prime 8tuplet (0,6,8,14,18,20,24,26) enumeration count 10,000 author WR A022545 Initial member of prime 9tuplet (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 8tuplet (0,2,6,8,12,18,20,26) enumeration count 10,000 author WR A022012 Initial member of prime 8tuplet (0,2,6,12,14,20,24,26) enumeration count 10,000 author WR A022013 Initial member of prime 8tuplet (0,6,8,14,18,20,24,26) enumeration count 10,000 author WR A022545 Initial member of prime 9tuplet (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 
20210523, 14:40  #149 
"Matthew Anderson"
Dec 2010
Oregon, USA
3×367 Posts 

20210907, 02:34  #150 
"Matthew Anderson"
Dec 2010
Oregon, USA
3×367 Posts 
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 
20210907, 03:02  #151 
If I May
"Chris Halsall"
Sep 2002
Barbados
10100011010011_{2} Posts 

20211018, 18:38  #152 
"Matthew Anderson"
Dec 2010
Oregon, USA
2115_{8} 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 
20211018, 20:46  #153 
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 20211018 at 20:46 Reason: pdf 
20211019, 02:33  #154  
"Matthew Anderson"
Dec 2010
Oregon, USA
3·367 Posts 
Quote:
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 9tuples  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 ktuplets. Cheers Matt Last fiddled with by MattcAnderson on 20211019 at 02:34 Reason: mispelled name 

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