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Message boards : Sieving : Basic math question for b value

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No.15Project donor
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Joined: 11 Jun 16
Posts: 26
ID: 449361
Credit: 929,881,217
RAC: 3,487
Discovered 2 mega primes321 LLR Silver: Earned 100,000 credits (404,375)Cullen LLR Gold: Earned 500,000 credits (748,151)ESP LLR Silver: Earned 100,000 credits (173,150)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,646,757)PPS LLR Ruby: Earned 2,000,000 credits (2,892,952)PSP LLR Ruby: Earned 2,000,000 credits (2,557,499)SoB LLR Sapphire: Earned 20,000,000 credits (22,766,851)SR5 LLR Ruby: Earned 2,000,000 credits (2,808,642)SGS LLR Silver: Earned 100,000 credits (266,982)TRP LLR Silver: Earned 100,000 credits (351,574)Woodall LLR Amethyst: Earned 1,000,000 credits (1,308,318)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (906,493)PPS Sieve Double Bronze: Earned 100,000,000 credits (111,307,049)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (34,122)AP 26/27 Sapphire: Earned 20,000,000 credits (20,683,988)GFN Double Gold: Earned 500,000,000 credits (759,170,896)PSA Amethyst: Earned 1,000,000 credits (1,853,420)
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 :)
____________
My Primes :) 3060772^262144+1 and 3673932^262144+1

Profile Michael GoetzProject donor
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Joined: 21 Jan 10
Posts: 13259
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The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,822,730)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Turquoise: Earned 5,000,000 credits (5,009,577)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Jade: Earned 10,000,000 credits (12,888,530)PSP LLR Turquoise: Earned 5,000,000 credits (5,197,957)SoB LLR Sapphire: Earned 20,000,000 credits (34,291,181)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (2,276,011)TRP LLR Ruby: Earned 2,000,000 credits (4,083,840)Woodall LLR Ruby: Earned 2,000,000 credits (2,195,123)321 Sieve Jade: Earned 10,000,000 credits (10,061,196)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (22,885,121)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Jade: Earned 10,000,000 credits (10,118,303)GFN Emerald: Earned 50,000,000 credits (72,383,585)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 112710 - Posted: 27 Dec 2017 | 19:13:01 UTC - in response to Message 112709.
Last modified: 27 Dec 2017 | 19:15:53 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 :)


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.15Project donor
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Joined: 11 Jun 16
Posts: 26
ID: 449361
Credit: 929,881,217
RAC: 3,487
Discovered 2 mega primes321 LLR Silver: Earned 100,000 credits (404,375)Cullen LLR Gold: Earned 500,000 credits (748,151)ESP LLR Silver: Earned 100,000 credits (173,150)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,646,757)PPS LLR Ruby: Earned 2,000,000 credits (2,892,952)PSP LLR Ruby: Earned 2,000,000 credits (2,557,499)SoB LLR Sapphire: Earned 20,000,000 credits (22,766,851)SR5 LLR Ruby: Earned 2,000,000 credits (2,808,642)SGS LLR Silver: Earned 100,000 credits (266,982)TRP LLR Silver: Earned 100,000 credits (351,574)Woodall LLR Amethyst: Earned 1,000,000 credits (1,308,318)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (906,493)PPS Sieve Double Bronze: Earned 100,000,000 credits (111,307,049)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (34,122)AP 26/27 Sapphire: Earned 20,000,000 credits (20,683,988)GFN Double Gold: Earned 500,000,000 credits (759,170,896)PSA Amethyst: Earned 1,000,000 credits (1,853,420)
Message 112712 - Posted: 27 Dec 2017 | 19:45:44 UTC - in response to Message 112710.
Last modified: 27 Dec 2017 | 19:46:09 UTC

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

Message boards : Sieving : Basic math question for b value

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