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Message boards : General discussion : Is there a 'probability of finding a prime' listed anywhere?

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Discovered 2 mega primes321 LLR Gold: Earned 500,000 credits (503,707)Cullen LLR Amethyst: Earned 1,000,000 credits (1,001,529)ESP LLR Gold: Earned 500,000 credits (502,172)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,028,459)PPS LLR Turquoise: Earned 5,000,000 credits (7,989,101)PSP LLR Gold: Earned 500,000 credits (566,759)SoB LLR Ruby: Earned 2,000,000 credits (2,047,598)SR5 LLR Amethyst: Earned 1,000,000 credits (1,014,245)SGS LLR Amethyst: Earned 1,000,000 credits (1,343,649)TRP LLR Amethyst: Earned 1,000,000 credits (1,279,172)Woodall LLR Amethyst: Earned 1,000,000 credits (1,017,620)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,005,090)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (32,970,234)PPS Sieve Sapphire: Earned 20,000,000 credits (31,771,675)AP 26/27 Ruby: Earned 2,000,000 credits (2,179,177)GFN Emerald: Earned 50,000,000 credits (87,116,853)PSA Turquoise: Earned 5,000,000 credits (8,743,250)
Message 115997 - Posted: 13 Mar 2018 | 23:29:18 UTC

Just wondering?

I'm fairly new to PrimeGrid and have approx 5 bronze and 1 Turquoise badge. I was just wondering if there is an 'overall' probability of finding a prime listed for each sub-project.

EG: 321 Prime search AVG 1 prime per 52,345 credit, Proth Prime search AVG 1 prime per 1,234 credit

It would give me some idea of how I'm tracking

(I also realise that a prime could be found with 1 credit or with 1 billion credits, but the average would be nice to know)

Thanx

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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 PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,132,712)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 Ruby: Earned 2,000,000 credits (2,234,442)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)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 (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,718,606)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,007,789)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 (10,118,303)GFN Emerald: Earned 50,000,000 credits (78,031,938)WW Sapphire: Earned 20,000,000 credits (32,204,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 115998 - Posted: 14 Mar 2018 | 0:13:59 UTC

The larger a number is, the harder it is to find a prime. The difficulty of finding a prime is roughly proportional to X^3 * ln(X), where X is the number of digits in the prime. So it's about 3000 times harder to find a million digit prime than it is to find a prime with one hundred thousand digits. This takes into account both the fact that larger primes are much rarer as well as taking much longer to run each individual test.

While I've never expressed it in terms of credit, on the smaller primes we do sometimes check the odds of a single test being prime.

The four smallest of our primality testing projects are, in order, GFN-15, SGS, PPSE, and GFN-16. As of last month, the odds of finding a prime in PPSE was about 1 in 14 thousand tests, and the odds of finding a GFN-16 were about 1 in 16 thousand tests. Those numbers are approximately 450 thousand and 500 thousand digits long, respectively.

Let's say your computer can do a PPSE test in 5 minutes. On average, then, you could expect to find one PPSE prime after about 48 days of testing.

We can extrapolate those odds for, say the ESP project. ESP numbers are about 7 times larger than PPSE, so it should take 7^3 * ln(7) times as long to find an ESP prime. That's 667 times longer, or 32037 days or about 88 years.
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Discovered 2 mega primes321 LLR Gold: Earned 500,000 credits (503,707)Cullen LLR Amethyst: Earned 1,000,000 credits (1,001,529)ESP LLR Gold: Earned 500,000 credits (502,172)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,028,459)PPS LLR Turquoise: Earned 5,000,000 credits (7,989,101)PSP LLR Gold: Earned 500,000 credits (566,759)SoB LLR Ruby: Earned 2,000,000 credits (2,047,598)SR5 LLR Amethyst: Earned 1,000,000 credits (1,014,245)SGS LLR Amethyst: Earned 1,000,000 credits (1,343,649)TRP LLR Amethyst: Earned 1,000,000 credits (1,279,172)Woodall LLR Amethyst: Earned 1,000,000 credits (1,017,620)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,005,090)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (32,970,234)PPS Sieve Sapphire: Earned 20,000,000 credits (31,771,675)AP 26/27 Ruby: Earned 2,000,000 credits (2,179,177)GFN Emerald: Earned 50,000,000 credits (87,116,853)PSA Turquoise: Earned 5,000,000 credits (8,743,250)
Message 115999 - Posted: 14 Mar 2018 | 0:32:44 UTC - in response to Message 115998.

Thanx for the explanation Michael.

You say you don't express in 'credits', you use 'tests' instead, are 'tests' equivalent to WU's?

Thanx again

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 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 PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,132,712)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 Ruby: Earned 2,000,000 credits (2,234,442)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)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 (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,718,606)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,007,789)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 (10,118,303)GFN Emerald: Earned 50,000,000 credits (78,031,938)WW Sapphire: Earned 20,000,000 credits (32,204,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 116000 - Posted: 14 Mar 2018 | 0:51:57 UTC - in response to Message 115999.

Thanx for the explanation Michael.

You say you don't express in 'credits', you use 'tests' instead, are 'tests' equivalent to WU's?

Thanx again


Yes.
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321 LLR Gold: Earned 500,000 credits (656,177)Cullen LLR Silver: Earned 100,000 credits (457,297)ESP LLR Silver: Earned 100,000 credits (437,502)PPS LLR Amethyst: Earned 1,000,000 credits (1,256,334)SoB LLR Amethyst: Earned 1,000,000 credits (1,246,109)SR5 LLR Ruby: Earned 2,000,000 credits (2,193,129)SGS LLR Silver: Earned 100,000 credits (101,658)Woodall LLR Silver: Earned 100,000 credits (292,129)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (32,498)PPS Sieve Jade: Earned 10,000,000 credits (15,515,229)AP 26/27 Amethyst: Earned 1,000,000 credits (1,491,867)GFN Ruby: Earned 2,000,000 credits (4,245,870)PSA Silver: Earned 100,000 credits (101,309)
Message 116004 - Posted: 14 Mar 2018 | 8:50:03 UTC - in response to Message 115998.

So it's about 3000 times harder to find a million digit prime than it is to find a prime with one hundred thousand digits.
<snip>
ESP numbers are about 7 times larger than PPSE, so it should take 7^3 * ln(7) times as long to find an ESP prime. That's 667 times longer, or 32037 days or about 88 years.

FYI, this is not how logs work. ln(x)/ln(y) <> ln(x/y). Of course, the answer is still in the right ball park (since the cube term is the dominant one).

[There is a bigger issue, in that, the size of the numbers are not fixed -- they grow. Hence the odds keep getting worse. Particularly severe for "sparse" projects like the conjecture ones]

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Discovered 6 mega primesEliminated 1 conjecture "k"Found 3 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 5 primes in the 2019 Tour de PrimesFound 6 primes in the 2020 Tour de PrimesFound 5 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (8,774,878)Cullen LLR Turquoise: Earned 5,000,000 credits (5,903,451)ESP LLR Turquoise: Earned 5,000,000 credits (7,207,880)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,122,074)PPS LLR Double Bronze: Earned 100,000,000 credits (100,874,964)PSP LLR Jade: Earned 10,000,000 credits (16,676,406)SoB LLR Sapphire: Earned 20,000,000 credits (20,019,367)SR5 LLR Sapphire: Earned 20,000,000 credits (25,605,231)SGS LLR Turquoise: Earned 5,000,000 credits (7,360,621)TPS LLR (retired) Bronze: Earned 10,000 credits (34,130)TRP LLR Sapphire: Earned 20,000,000 credits (21,424,369)Woodall LLR Turquoise: Earned 5,000,000 credits (8,171,820)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,236,219)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,383,853)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,626,419)PPS Sieve Emerald: Earned 50,000,000 credits (76,969,144)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (2,293,882)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,012,757)AP 26/27 Sapphire: Earned 20,000,000 credits (21,918,894)GFN Emerald: Earned 50,000,000 credits (77,695,028)WW Sapphire: Earned 20,000,000 credits (34,040,000)PSA Ruby: Earned 2,000,000 credits (2,939,755)
Message 116005 - Posted: 14 Mar 2018 | 9:25:12 UTC - in response to Message 115998.

The four smallest of our primality testing projects are, in order, GFN-15, SGS, PPSE, and GFN-16. As of last month, the odds of finding a prime in PPSE was about 1 in 14 thousand tests, and the odds of finding a GFN-16 were about 1 in 16 thousand tests. Those numbers are approximately 450 thousand and 500 thousand digits long, respectively.


Time for some statistical fail on my part. Are the odds above calculated from the earlier formula, or worked out from actual testing?

If we use the general formula, would sieving affect the practical outcome? Say you have a test range of candidates (pre-sieve), you could work out how many primes to expect in that range. After sieving, you would have the same number of expected primes, but a much shorter candidate list.

I didn't take statistics courses when offered as I thought I'd suck at it. Or do I suck at it because I didn't take those courses? Self fulfilling prophecy.

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (174,818)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (13,138,413)PSP LLR Silver: Earned 100,000 credits (428,457)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Ruby: Earned 2,000,000 credits (2,059,478)WW Turquoise: Earned 5,000,000 credits (9,640,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 116006 - Posted: 14 Mar 2018 | 9:34:12 UTC - in response to Message 116004.

ESP numbers are about 7 times larger than PPSE, so it should take 7^3 * ln(7) times as long to find an ESP prime. That's 667 times longer, or 32037 days or about 88 years.

FYI, this is not how logs work. ln(x)/ln(y) <> ln(x/y). Of course, the answer is still in the right ball park (since the cube term is the dominant one).


Right! If it goes as X^3 * ln X, it would be

(7X)^3 * ln (7X) = 7^3 * X^3 * (ln X + ln 7)

Since the ln 7 term will be negligible, it is more like 7^3 = 343 times slower.

/JeppeSN

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Discovered the World's First base 116 Generalized Cullen prime!!!Discovered 28 mega primesEliminated 7 conjecture "k"sDiscovered 1 Sophie Germain pairDiscovered 2 Fermat divisors2012 Tour de Primes highest prime count2012 Tour de Primes most Mountain Stage primes2015 Tour de Primes highest prime count2016 Tour de Primes highest prime countFound 23 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 2 primes in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes highest prime countFound 22 primes in the 2019 Tour de Primes2020 Tour de Primes highest prime scoreFound 21 primes in the 2020 Tour de PrimesFound 4 mega primes in the 2020 Tour de PrimesFound 8 primes in the 2021 Tour de PrimesFound 1 mega prime in the 2021 Tour de Primes321 LLR Double Silver: Earned 200,000,000 credits (201,403,028)Cullen LLR Double Silver: Earned 200,000,000 credits (201,409,561)ESP LLR Double Silver: Earned 200,000,000 credits (214,825,147)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (130,907,308)PPS LLR Double Gold: Earned 500,000,000 credits (735,383,613)PSP LLR Double Bronze: Earned 100,000,000 credits (171,559,468)SoB LLR Double Silver: Earned 200,000,000 credits (207,028,068)SR5 LLR Double Silver: Earned 200,000,000 credits (214,437,634)SGS LLR Double Silver: Earned 200,000,000 credits (205,718,935)TPS LLR (retired) Silver: Earned 100,000 credits (235,439)TRP LLR Double Silver: Earned 200,000,000 credits (201,215,056)Woodall LLR Double Silver: Earned 200,000,000 credits (201,651,344)321 Sieve (suspended) Double Silver: Earned 200,000,000 credits (235,451,253)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (83,794,448)Generalized Cullen/Woodall Sieve (suspended) Double Silver: Earned 200,000,000 credits (285,139,652)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,731,144,628)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Double Silver: Earned 200,000,000 credits (203,523,358)TRP Sieve (suspended) Double Silver: Earned 200,000,000 credits (201,489,157)AP 26/27 Double Silver: Earned 200,000,000 credits (435,073,808)GFN Double Ruby: Earned 2,000,000,000 credits (2,146,020,631)WW Double Ruby: Earned 2,000,000,000 credits (2,370,164,000)PSA Double Silver: Earned 200,000,000 credits (259,058,048)
Message 116010 - Posted: 14 Mar 2018 | 11:20:17 UTC - in response to Message 116004.
Last modified: 14 Mar 2018 | 11:21:07 UTC


[There is a bigger issue, in that, the size of the numbers are not fixed -- they grow. Hence the odds keep getting worse. Particularly severe for "sparse" projects like the conjecture ones]


I have often wondered about this in the sense that conjecture projects probably don't follow the same pattern as others. More specifically, assuming that the base of users doesn't change drastically (a safer assumption on conjectures where many users have particularly dedicated interests in such projects), as primes are found within a conjecture (thereby often reducing the number of candidates to be tested substantially), I suspect that the odds getting worse as primes grow is actually less severe than in non-conjecture projects (or at least follows a far less smoothed growth and potentially could even experience very slight, brief declines...at least in application if not in theory).

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Eliminated 1 conjecture "k"Found 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Silver: Earned 100,000 credits (229,492)Cullen LLR Silver: Earned 100,000 credits (110,733)PPS LLR Jade: Earned 10,000,000 credits (11,335,374)PSP LLR Silver: Earned 100,000 credits (104,385)SoB LLR Silver: Earned 100,000 credits (106,117)SR5 LLR Silver: Earned 100,000 credits (139,802)SGS LLR Amethyst: Earned 1,000,000 credits (1,325,207)TRP LLR Gold: Earned 500,000 credits (626,755)Woodall LLR Silver: Earned 100,000 credits (122,944)321 Sieve (suspended) Silver: Earned 100,000 credits (104,900)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,599)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (515,556)PPS Sieve Jade: Earned 10,000,000 credits (11,872,830)TRP Sieve (suspended) Silver: Earned 100,000 credits (255,612)AP 26/27 Ruby: Earned 2,000,000 credits (2,583,960)GFN Sapphire: Earned 20,000,000 credits (23,334,026)WW Amethyst: Earned 1,000,000 credits (1,088,000)PSA Turquoise: Earned 5,000,000 credits (7,522,050)
Message 116043 - Posted: 16 Mar 2018 | 11:03:58 UTC - in response to Message 116010.

Scott, I think that primes in CRUS bases also follow this rule, but since all prime searching stopped in then time when prime is found that is difficulty to prove.
On the other hand: I found primes on CRUS bases when it wasn't expected at all, and also cannot find prime in other bases where I should ( by prediction) find prime long time ago. So primes follows first rule: nobody doesn't know position ( where prime is located)
Also I found big difference in predicted number of primes, and real number in near-repdigit primes. But once again: it follow first rule :)
So CRUS maybe look "different" then other bases, but in real life it is just little more different then any other sequence we all search.
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