How do you efficiently sieve for prime 3/4-tuples?

[Puzzle-Peter]

It's me again. I am fooling around with customizing polysieve to be easier and more efficient for the respective constellation I want to search. Now I am running into an unexpected phenomenon.


I am sieving for very small primes (<1000 dd), so I don't need to sieve very far. That means, I sieve only to smallPrimes, and I am far below the max smallPrimes value. What is striking me as odd is that when I go below smallPrimes=100,000 it does get slower. Sieving less deeply saves time, but there seems to be a limit where it does not pay off any more. I suppose I haven't fully understood how bound_small_primes, SmallPrimes2 and denom work together so I am probably sabotaging myself. I played around with those values, but without success.


I would like to sieve only to (I guess 10,000 or 20,000) as a few more surviving candidates should be less time consuming than sieving ten times as deep. But somehow it doesn't work out.


Any hint on how to set the values mentioned above in relation to each other is greatly appreciated.


Peter

[henryzz]

Originally Posted by Puzzle-Peter

It's me again. I am fooling around with customizing polysieve to be easier and more efficient for the respective constellation I want to search. Now I am running into an unexpected phenomenon.


I am sieving for very small primes (<1000 dd), so I don't need to sieve very far. That means, I sieve only to smallPrimes, and I am far below the max smallPrimes value. What is striking me as odd is that when I go below smallPrimes=100,000 it does get slower. Sieving less deeply saves time, but there seems to be a limit where it does not pay off any more. I suppose I haven't fully understood how bound_small_primes, SmallPrimes2 and denom work together so I am probably sabotaging myself. I played around with those values, but without success.


I would like to sieve only to (I guess 10,000 or 20,000) as a few more surviving candidates should be less time consuming than sieving ten times as deep. But somehow it doesn't work out.


Any hint on how to set the values mentioned above in relation to each other is greatly appreciated.


Peter

The only reason I can think of for it getting slower with lower smallPrimes is it taking a while to write the output to disk.

bound_small_primes is basically the limit for the wheel sieve. It should allow you to ignore a lot of the search space.

Sometimes it is faster to sieve multiple primes at once. denom and SmallPrimes2 control how this is done. It may make it slower in some cases.

Could you tell me what command you are trying(PM if necessary)? I should be able to optimise the parameters for you.

[pepi37]

I was looking last and this month how Puzzle -Petter finds prime with n= on minus side. If I look k it is huge, and even huger must be number of left candidates. So I download and compile polysieve but found one problem: If I stop it before end, there is no output :(
So can it be fixed?
Also I am interested how many time is spent of making such sieve.