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Message boards : General discussion : Sieve factors

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Profile Skivelitis2
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Joined: 28 Mar 15
Posts: 49
ID: 388656
Credit: 704,649,171
RAC: 180,711
321 LLR Ruby: Earned 2,000,000 credits (2,625,709)Cullen LLR Ruby: Earned 2,000,000 credits (2,002,272)ESP LLR Ruby: Earned 2,000,000 credits (2,010,411)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,015,328)PPS LLR Ruby: Earned 2,000,000 credits (3,046,738)PSP LLR Turquoise: Earned 5,000,000 credits (5,032,920)SoB LLR Ruby: Earned 2,000,000 credits (2,044,307)SR5 LLR Ruby: Earned 2,000,000 credits (2,001,106)SGS LLR Ruby: Earned 2,000,000 credits (2,000,308)TRP LLR Ruby: Earned 2,000,000 credits (2,000,310)Woodall LLR Ruby: Earned 2,000,000 credits (2,004,881)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,048,750)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (10,013,479)PPS Sieve Double Silver: Earned 200,000,000 credits (341,620,511)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (500,162)TRP Sieve (suspended) Gold: Earned 500,000 credits (500,031)AP 26/27 Emerald: Earned 50,000,000 credits (50,003,824)GFN Emerald: Earned 50,000,000 credits (51,882,125)WW Double Silver: Earned 200,000,000 credits (203,296,000)
Message 87865 - Posted: 10 Sep 2015 | 11:58:11 UTC

To date I have completed 600+ ESP/PSP/SoB sieve workunits and have found 2 factors. Does this provide fodder for only 2 llr workunits? If so , I see how important these tasks are.
____________

Profile Michael GoetzProject donor
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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 2 mega primesFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de PrimesFound 2 primes in the 2022 Tour de PrimesFound 1 mega prime in the 2022 Tour de PrimesFound 1 prime in the 2022 Tour de Primes Mountain Stage321 LLR Turquoise: Earned 5,000,000 credits (6,638,389)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,094,541)PPS LLR Sapphire: Earned 20,000,000 credits (23,642,050)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (12,645,567)SGS LLR Turquoise: Earned 5,000,000 credits (5,037,630)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,032,821)321 Sieve (suspended) 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 (10,902,645)GFN Emerald: Earned 50,000,000 credits (92,455,703)WW Emerald: Earned 50,000,000 credits (65,888,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 87867 - Posted: 10 Sep 2015 | 12:54:18 UTC - in response to Message 87865.

To date I have completed 600+ ESP/PSP/SoB sieve workunits and have found 2 factors. Does this provide fodder for only 2 llr workunits? If so , I see how important these tasks are.



Every factor found by sieving is two LLR tasks that don't need to be run.
____________
My lucky number is 75898524288+1

Profile Skivelitis2
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Joined: 28 Mar 15
Posts: 49
ID: 388656
Credit: 704,649,171
RAC: 180,711
321 LLR Ruby: Earned 2,000,000 credits (2,625,709)Cullen LLR Ruby: Earned 2,000,000 credits (2,002,272)ESP LLR Ruby: Earned 2,000,000 credits (2,010,411)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,015,328)PPS LLR Ruby: Earned 2,000,000 credits (3,046,738)PSP LLR Turquoise: Earned 5,000,000 credits (5,032,920)SoB LLR Ruby: Earned 2,000,000 credits (2,044,307)SR5 LLR Ruby: Earned 2,000,000 credits (2,001,106)SGS LLR Ruby: Earned 2,000,000 credits (2,000,308)TRP LLR Ruby: Earned 2,000,000 credits (2,000,310)Woodall LLR Ruby: Earned 2,000,000 credits (2,004,881)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,048,750)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (10,013,479)PPS Sieve Double Silver: Earned 200,000,000 credits (341,620,511)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (500,162)TRP Sieve (suspended) Gold: Earned 500,000 credits (500,031)AP 26/27 Emerald: Earned 50,000,000 credits (50,003,824)GFN Emerald: Earned 50,000,000 credits (51,882,125)WW Double Silver: Earned 200,000,000 credits (203,296,000)
Message 87868 - Posted: 10 Sep 2015 | 13:09:44 UTC - in response to Message 87867.
Last modified: 10 Sep 2015 | 13:25:13 UTC

Ahhh had it backwards then. Still important however.

Edit: Does this mean a substantial amount of work has been greenlighted due to so few factors found or is it all a go until thus eliminated? I'm no math whiz so short answer ok. Sorry if this is covered in a FAQ somewhere.

Profile Michael GoetzProject donor
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Joined: 21 Jan 10
Posts: 13804
ID: 53948
Credit: 345,369,032
RAC: 1,967
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 2 mega primesFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de PrimesFound 2 primes in the 2022 Tour de PrimesFound 1 mega prime in the 2022 Tour de PrimesFound 1 prime in the 2022 Tour de Primes Mountain Stage321 LLR Turquoise: Earned 5,000,000 credits (6,638,389)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,094,541)PPS LLR Sapphire: Earned 20,000,000 credits (23,642,050)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (12,645,567)SGS LLR Turquoise: Earned 5,000,000 credits (5,037,630)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,032,821)321 Sieve (suspended) 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 (10,902,645)GFN Emerald: Earned 50,000,000 credits (92,455,703)WW Emerald: Earned 50,000,000 credits (65,888,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 87870 - Posted: 10 Sep 2015 | 13:54:31 UTC - in response to Message 87868.

Ahhh had it backwards then. Still important however.

Edit: Does this mean a substantial amount of work has been greenlighted due to so few factors found or is it all a go until thus eliminated? I'm no math whiz so short answer ok. Sorry if this is covered in a FAQ somewhere.


The latter.

You start with a set of numbers, and you don't know whether they're prime or composite. First you use a sieve, which works on the entire set of numbers at once, and it finds COMPOSITE numbers within that set. At the beginning, the sieve finds composite numbers very quickly, but as the sieving continues, it finds composite numbers more and more slowly. (We usually say it finds 'factors' -- it's actually determines that XXXXX is a factor of YYYYY, so saying it finds factors or it finds composite numbers is equally accurate.)

As each composite number is removed from the set of numbers you want to test, that set shrinks and shrinks and shrinks. All the while, the sieve is finding fewer and fewer factors. Eventually, it takes more computing time running the sieve to find a single factor than it does to run run LLR on one of the remaining numbers. At that point, you stop sieving and start testing each remaining unknown candidate with LLR to see if it's composite or if it's prime.

____________
My lucky number is 75898524288+1

numbermaniac
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Joined: 28 Mar 14
Posts: 197
ID: 305955
Credit: 13,077,710
RAC: 10,846
321 LLR Silver: Earned 100,000 credits (236,326)PPS LLR Ruby: Earned 2,000,000 credits (2,116,107)SR5 LLR Amethyst: Earned 1,000,000 credits (1,038,057)SGS LLR Ruby: Earned 2,000,000 credits (3,422,268)TRP LLR Gold: Earned 500,000 credits (502,390)321 Sieve (suspended) Gold: Earned 500,000 credits (512,303)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (503,510)PPS Sieve Ruby: Earned 2,000,000 credits (2,002,374)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (34,269)TRP Sieve (suspended) Bronze: Earned 10,000 credits (32,679)AP 26/27 Gold: Earned 500,000 credits (513,461)GFN Ruby: Earned 2,000,000 credits (2,010,259)PSA Silver: Earned 100,000 credits (141,661)
Message 88074 - Posted: 15 Sep 2015 | 6:50:47 UTC - in response to Message 87870.

Ahhh had it backwards then. Still important however.

Edit: Does this mean a substantial amount of work has been greenlighted due to so few factors found or is it all a go until thus eliminated? I'm no math whiz so short answer ok. Sorry if this is covered in a FAQ somewhere.


Eventually, it takes more computing time running the sieve to find a single factor than it does to run run LLR on one of the remaining numbers. At that point, you stop sieving and start testing each remaining unknown candidate with LLR to see if it's composite or if it's prime.

At what point does this occur? Sorry if it's a stupid question.

Profile Michael GoetzProject donor
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Joined: 21 Jan 10
Posts: 13804
ID: 53948
Credit: 345,369,032
RAC: 1,967
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 2 mega primesFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de PrimesFound 2 primes in the 2022 Tour de PrimesFound 1 mega prime in the 2022 Tour de PrimesFound 1 prime in the 2022 Tour de Primes Mountain Stage321 LLR Turquoise: Earned 5,000,000 credits (6,638,389)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,094,541)PPS LLR Sapphire: Earned 20,000,000 credits (23,642,050)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (12,645,567)SGS LLR Turquoise: Earned 5,000,000 credits (5,037,630)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,032,821)321 Sieve (suspended) 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 (10,902,645)GFN Emerald: Earned 50,000,000 credits (92,455,703)WW Emerald: Earned 50,000,000 credits (65,888,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 88083 - Posted: 15 Sep 2015 | 12:26:28 UTC - in response to Message 88074.

Ahhh had it backwards then. Still important however.

Edit: Does this mean a substantial amount of work has been greenlighted due to so few factors found or is it all a go until thus eliminated? I'm no math whiz so short answer ok. Sorry if this is covered in a FAQ somewhere.


Eventually, it takes more computing time running the sieve to find a single factor than it does to run run LLR on one of the remaining numbers. At that point, you stop sieving and start testing each remaining unknown candidate with LLR to see if it's composite or if it's prime.

At what point does this occur? Sorry if it's a stupid question.


Hmmmmm. You actually quoted the answer to your question: When it takes more time to remove a factor from the sieve than it does to check a number with LLR or Genefer, then it's time to stop sieving.

While it's possible to figure out mathematically when that will occur based on how fast the sieve runs, how fast LLR runs, how the factor density changes as the sieve gets deeper, and how long each number takes to compute with LLR based on the size of the number, in practice the speeds of both the sieving and LLR change over time because of hardware and software improvements. So forward looking calculations ("We'll stop when we get to point X") tend to only be valid until the next software or hardware inovation, and then everything changes. In practice, it's more like "We seem to be finding factors more slowly now than we can test numbers with LLR, so it's time to stop sieving".
____________
My lucky number is 75898524288+1

numbermaniac
Volunteer tester
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Joined: 28 Mar 14
Posts: 197
ID: 305955
Credit: 13,077,710
RAC: 10,846
321 LLR Silver: Earned 100,000 credits (236,326)PPS LLR Ruby: Earned 2,000,000 credits (2,116,107)SR5 LLR Amethyst: Earned 1,000,000 credits (1,038,057)SGS LLR Ruby: Earned 2,000,000 credits (3,422,268)TRP LLR Gold: Earned 500,000 credits (502,390)321 Sieve (suspended) Gold: Earned 500,000 credits (512,303)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (503,510)PPS Sieve Ruby: Earned 2,000,000 credits (2,002,374)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (34,269)TRP Sieve (suspended) Bronze: Earned 10,000 credits (32,679)AP 26/27 Gold: Earned 500,000 credits (513,461)GFN Ruby: Earned 2,000,000 credits (2,010,259)PSA Silver: Earned 100,000 credits (141,661)
Message 88163 - Posted: 16 Sep 2015 | 8:35:04 UTC - in response to Message 88083.

Ahhh had it backwards then. Still important however.

Edit: Does this mean a substantial amount of work has been greenlighted due to so few factors found or is it all a go until thus eliminated? I'm no math whiz so short answer ok. Sorry if this is covered in a FAQ somewhere.


Eventually, it takes more computing time running the sieve to find a single factor than it does to run run LLR on one of the remaining numbers. At that point, you stop sieving and start testing each remaining unknown candidate with LLR to see if it's composite or if it's prime.

At what point does this occur? Sorry if it's a stupid question.


Hmmmmm. You actually quoted the answer to your question: When it takes more time to remove a factor from the sieve than it does to check a number with LLR or Genefer, then it's time to stop sieving.

While it's possible to figure out mathematically when that will occur based on how fast the sieve runs, how fast LLR runs, how the factor density changes as the sieve gets deeper, and how long each number takes to compute with LLR based on the size of the number, in practice the speeds of both the sieving and LLR change over time because of hardware and software improvements. So forward looking calculations ("We'll stop when we get to point X") tend to only be valid until the next software or hardware inovation, and then everything changes. In practice, it's more like "We seem to be finding factors more slowly now than we can test numbers with LLR, so it's time to stop sieving".


Yeah, I know I kinda quoted it but I was asking when, like an actual date rather than "when this happens." But yeah, I see what you mean. Thanks :)

Message boards : General discussion : Sieve factors

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