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 2017-11-05, 20:35 #1 bhelmes     Mar 2016 52·13 Posts a primesieve? A peaceful evening for all, Is it possible to find a prime generating sieving algorithm for the following described function: http://devalco.de/poly_xy.php Have a lot of fun Bernhard
2017-11-05, 22:40   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by bhelmes A peaceful evening for all, Is it possible to find a prime generating sieving algorithm for the following described function: http://devalco.de/poly_xy.php Have a lot of fun Bernhard
do your own work ... also a quick PARI/GP script shows these are the u,v pairs mod 6 that work to give a possible prime greater than 3.

Quote:
 0,1 0,5 1,0 1,2 1,4 2,1 2,3 2,5 3,2 3,4 4,1 4,3 4,5 5,0 5,2 5,4

2017-11-08, 15:27   #3
bhelmes

Mar 2016

52·13 Posts

A peaceful day for all,

Quote:
 Originally Posted by science_man_88 do your own work ... also a quick PARI/GP script shows these are the u,v pairs mod 6 that work to give a possible prime greater than 3.
The described primes are also p+/-1=0 mod 8

Hint 1: Fix either u or v for the function f(u,v) and examine the prime distribution. There is a pattern, you could find.

http://devalco.de/poly_xy.php

Have a lot of fun by examing the prime distribution
Bernhard

2017-11-11, 18:54   #4
bhelmes

Mar 2016

52·13 Posts

Quote:
 Originally Posted by bhelmes A peaceful day for all, Hint 1: Fix either u or v for the function f(u,v) and examine the prime distribution. There is a pattern, you could find.
Hint 2: Consider for f(u,v)=f(u, u-1), there is an explication for a primesieve concerning f(n)=2n^2-1 : http://devalco.de/quadr_Sieb_2x%5E2-1.php

You can use this primesieve for a better primesieve concerning
http://devalco.de/poly_xy.php

There will be a third hint in some few days, and concerning the participation a suggestion for a first solution.

There might be several solution, you have the first choice
Greeting from the primes
Bernhard

2017-11-11, 20:12   #5
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by bhelmes A peaceful day for all, The described primes are also p+/-1=0 mod 8 Hint 1: Fix either u or v for the function f(u,v) and examine the prime distribution. There is a pattern, you could find. http://devalco.de/poly_xy.php Have a lot of fun by examing the prime distribution Bernhard
if there's a pattern you know about then just do it, and stop posting it where I have to look at it then ?? you seem too much like me.

 2017-11-11, 20:30 #6 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22×7×337 Posts This looks like Misc.Math. (it is obviously not a puzzle, just a bunch of fluff plus shameless self-promotion to boot.)
 2017-11-14, 18:51 #7 bhelmes     Mar 2016 52×13 Posts "Anyone who has "discovered" a pattern or found order in disorder,ie. feigenbaum constants, are justified in feeling a sense of pride and accomplishment for this personal insight. " from jwaltos (http://www.mersenneforum.org/showpos...9&postcount=25) I am very thankful for these words. An explication for the proposed pattern for the function f(u,v)=u^2 + 2uv - v2 : You can simplify by fixing either u or v and you get a quadratic function with one variable. You could use this "slices" horizontal and vertikal. for every p with p | f(n)=an^2+bn+c (a<5; a,b,c element N) follows that p | f(n+p) and p | f(-n-b/a) The primes p with p | f(u,v) appears double periodically horizantal and vertikal. In order to understand this i have tried to give an "amazing" applet http://devalco.de/poly_xy.php you can click on the primes 7, 17, 23, 31 and so on The primes p of the function f(u,v)=u^2 + 2uv - v2 build corally a pattern. The remaining question is: in which order you can make a sieving (dividing by the primes) As the pattern is clear, the solution for the algorithm will come in 3 days. Bernhard @Batalov I support Gimps, LL-D test place 164
2017-11-14, 21:44   #8
CRGreathouse

Aug 2006

135418 Posts

Quote:
 Originally Posted by bhelmes An explication for the proposed pattern for the function f(u,v)=u^2 + 2uv - v2
If I understand you correctly, this is A038873, 2 together with primes ±1 mod 8.

2017-11-14, 22:00   #9
bhelmes

Mar 2016

5058 Posts

Quote:
 Originally Posted by CRGreathouse If I understand you correctly, this is A038873, 2 together with primes ±1 mod 8.
Right

 2017-11-17, 21:09 #10 bhelmes     Mar 2016 52·13 Posts A peaceful evening for all, a proposition for a primesieve concerning f(u, v)=u² + 2uv -v² : 1. Make a primesieve concerning the function f(u, u-1) = 2u²-1 from u=2 to u_max (there is a detailled description under http://devalco.de/quadr_Sieb_2x%5E2-1.php Safe all sieved out primes p with p < u_max, these primes appear in all quadratic functions with f(u, v) where u goes from 2 to u_max. (This should be the amount Q) 2. Make a sieving (vertikal) for f(u, 1)= u²+2u-1 by using the presieved primes Q 3. Make a sieving (vertikal) for f(u, 2)= u²+4u-4 by using the presieved primes Q 4. Make a sieving (vertikal) for f(u, 3)= u²+6u-9 by using the presieved primes Q .... u-2. Make a sieving (vertikal) for f(u, u-2)= u²+2(u-1)-(u-2)² by using the presieved primes Q The sieving is made by dividing the function f(u,v) by the primes Q. Do you have any idea why this prime sieve could be better than the prime generator for the function f(n)=2n²-1 ? @Batalov It looks like Misc. Math is a cold, dark and windy place, do you have a more decent place for the thread ? Or please give a mathematical reason.

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