Prime Constellations 2

[MattcAnderson]

Hi Internet,

Today I made some more examples about k-tuples.
You can see my Google Sites webpage.

https://sites.google.com/site/3tuples/

I am open to feedback.

Regards,
Matt

[MattcAnderson]

Hi Internet,

Here is a Maple page for a prime cluster.

Regards,
Matt

[danaj]

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.

[bhelmes]

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.


Greetings from the quadratic polynomials
Bernhard