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Message boards : Sieving : Basic math question for b value

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No.15

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Message 112709 - Posted: 27 Dec 2017 | 18:47:43 UTC

So I am new to this but I am determined to learn the math behind the different projects at primgrid.

Currently I am doing sieving for gfn22 and would like to understand how the b value affects the computation. Can someone point me to a primer or explain it in high school math level terms. I am sorry for my denseness but HS math was +25 years ago for me :)
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Michael Goetz
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Message 112710 - Posted: 27 Dec 2017 | 19:13:01 UTC - in response to Message 112709.

So I am new to this but I am determined to learn the math behind the different projects at primgrid.

Currently I am doing sieving for gfn22 and would like to understand how the b value affects the computation. Can someone point me to a primer or explain it in high school math level terms. I am sorry for my denseness but HS math was +25 years ago for me :)

I'll take a stab at this...

First of all, let's get the nomenclature consistent so we're talking about the same thing. There's two different meanings for "n", so...

GFN's are of the form b^n+1, where n must be a power of 2, or, alternatively, b^2^N+1 (i.e., n=2^N).

In "GFN22", the "22" is "N", so you're talking about numbers of the form b^2^22+1 or b^4194304+1.

Assuming N is constant, the size of the number is proportional to log(b), as is the duration of the calculation. Is that what you meant by "how the b value affects the computation"?

On the other hand, were you talking about the command line argument to the sieve program? That's got nothing to do with math. That's the blocking factor for how large the GPU kernels (blocks of work) will be. Really low numbers are inefficient, but really high numbers cause lots of screen lag and/or can crash the video driver. Inefficiency increases a LOT at the lower values, but doesn't change much at the higher values. Conversely, lag increases a LOT at the higher values, but doesn't change much at the lower values. The middle values are therefore a very good compromise between efficiency and usability: you don't gain much by setting B very high, but the computer becomes unusable.
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No.15

Joined: 11 Jun 16
Posts: 26
ID: 449361
Credit: 931,713,491
RAC: 0

Message 112712 - Posted: 27 Dec 2017 | 19:45:44 UTC - in response to Message 112710.

Yes the first explanation is what I meant although I did wonder about the cmd line b value as well.

I think I got it, I'll read it a few times and try and get a good picture of what it is doing. I'll see if I can read some stuff on mathworld as well.

Thanks!
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My Primes :) 3060772^262144+1 and 3673932^262144+1

Message boards : Sieving : Basic math question for b value