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Message boards : Aggie The Pew message board : Residue

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CaravaggioProject donor
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Joined: 15 May 11
Posts: 656
ID: 98704
Credit: 42,707,395
RAC: 0
321 LLR Silver: Earned 100,000 credits (346,575)Cullen LLR Silver: Earned 100,000 credits (119,890)PPS LLR Amethyst: Earned 1,000,000 credits (1,149,242)PSP LLR Silver: Earned 100,000 credits (161,710)SoB LLR Bronze: Earned 10,000 credits (13,000)SGS LLR Gold: Earned 500,000 credits (633,326)TRP LLR Silver: Earned 100,000 credits (224,572)Woodall LLR Silver: Earned 100,000 credits (275,235)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (6,879,611)PPS Sieve Sapphire: Earned 20,000,000 credits (27,663,307)GFN Gold: Earned 500,000 credits (638,284)PSA Ruby: Earned 2,000,000 credits (4,600,255)
Message 37674 - Posted: 30 Jun 2011 | 1:15:40 UTC

OK, ok, I'm exposing my ignorance. When a wu is complete, and is not a prime, it often refers to the Residue = XXXaXXXXXabcXd etc. What is the Residue?

If anyone can explain residue, say, in terms of beer or pizza, it would be appreciated.

Thanks,

C

Profile Mark DoomProject donor
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Joined: 21 Jan 11
Posts: 629
ID: 82310
Credit: 132,563,921
RAC: 0
Discovered 1 Fermat divisor321 LLR Amethyst: Earned 1,000,000 credits (1,044,451)Cullen LLR Amethyst: Earned 1,000,000 credits (1,012,570)PPS LLR Ruby: Earned 2,000,000 credits (2,818,774)PSP LLR Silver: Earned 100,000 credits (123,174)SoB LLR Jade: Earned 10,000,000 credits (18,119,601)SR5 LLR Gold: Earned 500,000 credits (519,595)SGS LLR Turquoise: Earned 5,000,000 credits (9,292,019)TRP LLR Amethyst: Earned 1,000,000 credits (1,552,511)Woodall LLR Silver: Earned 100,000 credits (296,881)Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,218,011)PPS Sieve Emerald: Earned 50,000,000 credits (63,008,001)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (884,469)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,608,252)GFN Turquoise: Earned 5,000,000 credits (8,987,564)PSA Ruby: Earned 2,000,000 credits (3,077,926)
Message 37677 - Posted: 30 Jun 2011 | 3:13:09 UTC - in response to Message 37674.

Not sure..but I've been leaving a lot of residue behind at this party..

Iain BethuneProject donor
Honorary cruncher
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Joined: 28 Jan 09
Posts: 1588
ID: 34775
Credit: 194,056,043
RAC: 0
321 LLR Gold: Earned 500,000 credits (597,175)Cullen LLR Amethyst: Earned 1,000,000 credits (1,355,381)ESP LLR Turquoise: Earned 5,000,000 credits (5,048,594)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,564,412)PPS LLR Amethyst: Earned 1,000,000 credits (1,025,115)PSP LLR Sapphire: Earned 20,000,000 credits (28,367,849)SoB LLR Jade: Earned 10,000,000 credits (16,215,329)SR5 LLR Turquoise: Earned 5,000,000 credits (5,189,992)SGS LLR Amethyst: Earned 1,000,000 credits (1,244,067)TRP LLR Turquoise: Earned 5,000,000 credits (5,169,405)Woodall LLR Amethyst: Earned 1,000,000 credits (1,070,956)321 Sieve Bronze: Earned 10,000 credits (20,003)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (200,371)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (11,645,025)PPS Sieve Turquoise: Earned 5,000,000 credits (7,536,532)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,017,144)TRP Sieve (suspended) Gold: Earned 500,000 credits (554,946)AP 26/27 Ruby: Earned 2,000,000 credits (3,577,848)GFN Emerald: Earned 50,000,000 credits (97,047,976)PSA Ruby: Earned 2,000,000 credits (4,606,694)
Message 37679 - Posted: 30 Jun 2011 | 7:55:28 UTC - in response to Message 37677.

Explanation follows (skip to the third paragraph if you want to know the beer analogy)

When you do an LLR test you start with some small initial number then repeatedly square it and subtract 2 for (n-2) iterations (where n is the n in k*2^n - 1) - this is the iteration counter you see when you running a test on PRPNet.

Clearly the numbers involved get pretty big (even though you do all the arithmetic modulo the prime number you are testing). So, when you get to the end of the iterations, you look at the number you have left - if it is zero, then you have found a prime, if not, then you have a composite, and a large non-zero number. What the residue is is just the lowest 64 bits of the big number - enough that if two computers do the test and come up with the same residue then we can be sure they have done a correct calculation to very high level of confidence.

In terms of beer, you could think of the residue as being a small sample taken from a large tank at the end of the brewing process - it would be impractical to sample the entire tank before bottling and distributing it. Just by looking at a small sample, we can be fairly sure about the rest...

See wikipedia for a full description of the LLR test: http://en.wikipedia.org/wiki/Lucas–Lehmer–Riesel_test

Cheers

- Iain


____________
Twitter: IainBethune
Proud member of team "Aggie The Pew". Go Aggie!
3073428256125*2^1290000-1 is Prime!

CaravaggioProject donor
Send message
Joined: 15 May 11
Posts: 656
ID: 98704
Credit: 42,707,395
RAC: 0
321 LLR Silver: Earned 100,000 credits (346,575)Cullen LLR Silver: Earned 100,000 credits (119,890)PPS LLR Amethyst: Earned 1,000,000 credits (1,149,242)PSP LLR Silver: Earned 100,000 credits (161,710)SoB LLR Bronze: Earned 10,000 credits (13,000)SGS LLR Gold: Earned 500,000 credits (633,326)TRP LLR Silver: Earned 100,000 credits (224,572)Woodall LLR Silver: Earned 100,000 credits (275,235)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (6,879,611)PPS Sieve Sapphire: Earned 20,000,000 credits (27,663,307)GFN Gold: Earned 500,000 credits (638,284)PSA Ruby: Earned 2,000,000 credits (4,600,255)
Message 37682 - Posted: 30 Jun 2011 | 9:25:44 UTC - in response to Message 37679.

Iain, you are my hero! (for the day.) That was lucid and concise. Though it wasn't necessary, I appreciate the beer analogy and thank you for the effort.

-C

Profile Gary Craig
Volunteer tester
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Joined: 30 Dec 09
Posts: 3213
ID: 52890
Credit: 1,005,618,748
RAC: 0
Discovered 1 mega prime321 LLR Ruby: Earned 2,000,000 credits (2,893,273)Cullen LLR Ruby: Earned 2,000,000 credits (2,440,687)ESP LLR Turquoise: Earned 5,000,000 credits (5,738,876)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (6,292,626)PPS LLR Turquoise: Earned 5,000,000 credits (9,648,951)PSP LLR Turquoise: Earned 5,000,000 credits (5,653,927)SoB LLR Jade: Earned 10,000,000 credits (10,558,341)SR5 LLR Turquoise: Earned 5,000,000 credits (5,748,705)SGS LLR Ruby: Earned 2,000,000 credits (3,335,713)TRP LLR Jade: Earned 10,000,000 credits (12,602,818)Woodall LLR Ruby: Earned 2,000,000 credits (2,282,622)321 Sieve Gold: Earned 500,000 credits (740,566)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (59,788,598)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,143,068)PPS Sieve Double Gold: Earned 500,000,000 credits (524,673,938)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,130,821)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (10,074,710)AP 26/27 Sapphire: Earned 20,000,000 credits (43,842,888)GFN Double Silver: Earned 200,000,000 credits (224,648,943)PSA Emerald: Earned 50,000,000 credits (62,378,755)
Message 37759 - Posted: 1 Jul 2011 | 7:47:24 UTC - in response to Message 37682.

Iain, you are my hero! (for the day.) That was lucid and concise. Though it wasn't necessary, I appreciate the beer analogy and thank you for the effort.

-C

I like beer analogies.

It occurs to me that I could have omitted the word "analogies" from that sentence and it would still be grammatically correct and even more true.

--Gary

Message boards : Aggie The Pew message board : Residue

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