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Message boards : Proth Prime Search : Type of prime?

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Profile mattozanProject donor
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Discovered 2 mega primesFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain StageFound 4 primes in the 2019 Tour de PrimesFound 2 primes in the 2019 Tour de Primes Mountain Stage2020 Tour de Primes most Mountain Stage primesFound 3 primes in the 2020 Tour de PrimesFound 2 primes in the 2020 Tour de Primes Mountain Stage321 LLR Turquoise: Earned 5,000,000 credits (5,173,611)Cullen LLR Amethyst: Earned 1,000,000 credits (1,663,005)ESP LLR Turquoise: Earned 5,000,000 credits (8,666,319)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,621,320)PPS LLR Emerald: Earned 50,000,000 credits (69,391,290)PSP LLR Sapphire: Earned 20,000,000 credits (20,147,770)SoB LLR Jade: Earned 10,000,000 credits (14,595,713)SR5 LLR Sapphire: Earned 20,000,000 credits (25,053,612)SGS LLR Jade: Earned 10,000,000 credits (14,681,661)TRP LLR Turquoise: Earned 5,000,000 credits (9,238,331)Woodall LLR Amethyst: Earned 1,000,000 credits (1,534,611)321 Sieve Ruby: Earned 2,000,000 credits (2,421,223)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,165,870)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,012,635)PPS Sieve Double Silver: Earned 200,000,000 credits (462,698,170)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (727,064)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,187,678)AP 26/27 Double Bronze: Earned 100,000,000 credits (100,614,098)GFN Double Silver: Earned 200,000,000 credits (219,728,875)PSA Emerald: Earned 50,000,000 credits (52,388,050)
Message 44749 - Posted: 12 Dec 2011 | 20:59:46 UTC

I just found 2175*2^749073+1 is prime.

Is there any way to figure out more properties of this prime?

With so many different types of primes in PrimeGrid projects, how can I figure out if this one is in any of those categories?


    Twin Prime? (probably not)
    Euler Prime?
    Emirp Prime? (should be easy enough to check, somehow)
    Mersenne Prime (IIRC, this must be a Mersenne Prime if it was validated by LLR?)
    Fermat Prime?
    Cullen Prime?
    Woodall Prime?
    Sophie Germain Prime?


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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 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 (15,527,037)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 (2,276,330)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)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 (74,703,799)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 44755 - Posted: 12 Dec 2011 | 21:28:22 UTC - in response to Message 44749.

I just found 2175*2^749073+1 is prime.

Is there any way to figure out more properties of this prime?

With so many different types of primes in PrimeGrid projects, how can I figure out if this one is in any of those categories?

    Twin Prime? (probably not)
    Euler Prime?
    Emirp Prime? (should be easy enough to check, somehow)
    Mersenne Prime (IIRC, this must be a Mersenne Prime if it was validated by LLR?)
    Fermat Prime?
    Cullen Prime?
    Woodall Prime?
    Sophie Germain Prime?



The easiest way to answer your questions would be to first understand what those types of primes are. Since many of them require that the number be of a specific form, if the prime you found isn't of that form, then it's not that type of prime.

For example, Mersenne Primes are of the form 2^n-1. Your number isn't of that form, so it's not a Mersenne Prime. Likewise, it's not a Fermat (2^2^n+1) or a Generalized Fermat Number (b^2^n+1), or a Cullen (n*2^n+1) or Woodall (n*2^n-1) number.

It is a Proth prime, which is of the form k*2^n+1.

Mersenne Prime (IIRC, this must be a Mersenne Prime if it was validated by LLR?)


The LLR test is used for primes of the form k*2^n-1. The Proth test is used for Proth primes (such as yours) of the form k*2^n+1. The LLR program that we use (not to be confused with the LLR test, which is an algorithm), is capable of performing both the LLR test and the Proth test on appropriate numbers. (It can also test GFN numbers, which is yet another test.)

Is there any way to figure out more properties of this prime?


You may have noticed that sometimes people do additional tests on some of the primes that are found.

Sometimes, the Proth primes are divisors of Fermat Numbers, Generalized Fermat Numbers, or Extended Generalized Fermat Numbers.

The PFGW64 program can test to see if the prime is one of those divisors. It's a pretty time consuming computation. My understanding is that those tests are automatically run on the PrimeGrid servers when the prime is discovered. If it's found to also be a divisor of one of those special numbers, it's noted in the email that's sent to you.


____________
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Profile mattozanProject donor
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Discovered 2 mega primesFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain StageFound 4 primes in the 2019 Tour de PrimesFound 2 primes in the 2019 Tour de Primes Mountain Stage2020 Tour de Primes most Mountain Stage primesFound 3 primes in the 2020 Tour de PrimesFound 2 primes in the 2020 Tour de Primes Mountain Stage321 LLR Turquoise: Earned 5,000,000 credits (5,173,611)Cullen LLR Amethyst: Earned 1,000,000 credits (1,663,005)ESP LLR Turquoise: Earned 5,000,000 credits (8,666,319)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,621,320)PPS LLR Emerald: Earned 50,000,000 credits (69,391,290)PSP LLR Sapphire: Earned 20,000,000 credits (20,147,770)SoB LLR Jade: Earned 10,000,000 credits (14,595,713)SR5 LLR Sapphire: Earned 20,000,000 credits (25,053,612)SGS LLR Jade: Earned 10,000,000 credits (14,681,661)TRP LLR Turquoise: Earned 5,000,000 credits (9,238,331)Woodall LLR Amethyst: Earned 1,000,000 credits (1,534,611)321 Sieve Ruby: Earned 2,000,000 credits (2,421,223)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,165,870)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,012,635)PPS Sieve Double Silver: Earned 200,000,000 credits (462,698,170)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (727,064)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,187,678)AP 26/27 Double Bronze: Earned 100,000,000 credits (100,614,098)GFN Double Silver: Earned 200,000,000 credits (219,728,875)PSA Emerald: Earned 50,000,000 credits (52,388,050)
Message 44765 - Posted: 12 Dec 2011 | 22:21:50 UTC - in response to Message 44755.

Thank you for such an informative reply! The distinction between the LLR test and program was also very helpful.

After I wrapped my head around the concept, I realized my prime is also excluded from being a Emirp by virtue of starting with "6."

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321 LLR Bronze: Earned 10,000 credits (11,773)Cullen LLR Bronze: Earned 10,000 credits (14,945)ESP LLR Bronze: Earned 10,000 credits (26,855)PPS LLR Bronze: Earned 10,000 credits (84,876)PSP LLR Bronze: Earned 10,000 credits (15,311)SoB LLR Bronze: Earned 10,000 credits (21,440)SR5 LLR Bronze: Earned 10,000 credits (29,270)SGS LLR Bronze: Earned 10,000 credits (26,616)TPS LLR (retired) Bronze: Earned 10,000 credits (36,288)TRP LLR Bronze: Earned 10,000 credits (41,655)Woodall LLR Bronze: Earned 10,000 credits (15,807)321 Sieve Bronze: Earned 10,000 credits (20,014)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (23,405)PPS Sieve Bronze: Earned 10,000 credits (36,192)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (20,306)TRP Sieve (suspended) Bronze: Earned 10,000 credits (21,738)GFN Bronze: Earned 10,000 credits (86,217)PSA Ruby: Earned 2,000,000 credits (2,143,756)
Message 44771 - Posted: 12 Dec 2011 | 22:38:02 UTC - in response to Message 44749.

I just found 2175*2^749073+1 is prime.

Is there any way to figure out more properties of this prime?

    Twin Prime? (probably not)


The prime was not tested for twin. You can manually do this by testing the -1 form. In this case, 2175*2^749073-1.
____________

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Discovered 2 mega primesFound 1 prime in the 2019 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,334,077)Cullen LLR Turquoise: Earned 5,000,000 credits (5,010,955)ESP LLR Turquoise: Earned 5,000,000 credits (7,439,418)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,501,906)PPS LLR Sapphire: Earned 20,000,000 credits (26,697,006)PSP LLR Turquoise: Earned 5,000,000 credits (6,184,417)SoB LLR Jade: Earned 10,000,000 credits (12,120,365)SR5 LLR Turquoise: Earned 5,000,000 credits (9,234,440)SGS LLR Turquoise: Earned 5,000,000 credits (5,201,403)TRP LLR Turquoise: Earned 5,000,000 credits (5,628,223)Woodall LLR Turquoise: Earned 5,000,000 credits (5,061,985)321 Sieve Amethyst: Earned 1,000,000 credits (1,027,534)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (17,370,919)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,014,372)PPS Sieve Double Bronze: Earned 100,000,000 credits (129,430,775)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,083,315)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,629,248)AP 26/27 Emerald: Earned 50,000,000 credits (56,876,924)GFN Double Silver: Earned 200,000,000 credits (286,079,854)PSA Double Silver: Earned 200,000,000 credits (200,556,062)
Message 45049 - Posted: 17 Dec 2011 | 5:05:34 UTC - in response to Message 44755.

snip...
Sometimes, the Proth primes are divisors of Fermat Numbers, Generalized Fermat Numbers, or Extended Generalized Fermat Numbers.

The PFGW64 program can test to see if the prime is one of those divisors. It's a pretty time consuming computation. My understanding is that those tests are automatically run on the PrimeGrid servers when the prime is discovered. If it's found to also be a divisor of one of those special numbers, it's noted in the email that's sent to you.

Is this an example of this?

Added 103718 : 423*2^1105874+1 (332904 digits) Divides GF(1105872,8)

Got it today and it's a first for me I believe.
____________

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 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 (15,527,037)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 (2,276,330)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)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 (74,703,799)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 45064 - Posted: 17 Dec 2011 | 12:57:26 UTC - in response to Message 45049.

Is this an example of this?

Added 103718 : 423*2^1105874+1 (332904 digits) Divides GF(1105872,8)

Got it today and it's a first for me I believe.


Yeah, looks like it. Grats!


____________
My lucky number is 75898524288+1

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321 LLR Bronze: Earned 10,000 credits (11,773)Cullen LLR Bronze: Earned 10,000 credits (14,945)ESP LLR Bronze: Earned 10,000 credits (26,855)PPS LLR Bronze: Earned 10,000 credits (84,876)PSP LLR Bronze: Earned 10,000 credits (15,311)SoB LLR Bronze: Earned 10,000 credits (21,440)SR5 LLR Bronze: Earned 10,000 credits (29,270)SGS LLR Bronze: Earned 10,000 credits (26,616)TPS LLR (retired) Bronze: Earned 10,000 credits (36,288)TRP LLR Bronze: Earned 10,000 credits (41,655)Woodall LLR Bronze: Earned 10,000 credits (15,807)321 Sieve Bronze: Earned 10,000 credits (20,014)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (23,405)PPS Sieve Bronze: Earned 10,000 credits (36,192)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (20,306)TRP Sieve (suspended) Bronze: Earned 10,000 credits (21,738)GFN Bronze: Earned 10,000 credits (86,217)PSA Ruby: Earned 2,000,000 credits (2,143,756)
Message 48112 - Posted: 29 Jan 2012 | 21:11:20 UTC - in response to Message 46611.

So when could we expect to see a long computational time for a PPS LLR as a result of the sieving process? Is it possible to find a megaprime by means or from the PPS LLR search?

Long run times happen depending on the range being searched. All the ranges in the Proth Prime Search can be viewed here.

As for a specific Mega Prime search, you can see that one of the ports in PRPNet is dedicated to this.
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321 LLR Ruby: Earned 2,000,000 credits (2,050,605)Cullen LLR Silver: Earned 100,000 credits (104,070)ESP LLR Amethyst: Earned 1,000,000 credits (1,018,623)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (198,013)PPS LLR Amethyst: Earned 1,000,000 credits (1,642,058)PSP LLR Gold: Earned 500,000 credits (897,619)SoB LLR Amethyst: Earned 1,000,000 credits (1,683,694)SR5 LLR Amethyst: Earned 1,000,000 credits (1,002,127)SGS LLR Gold: Earned 500,000 credits (580,961)TRP LLR Amethyst: Earned 1,000,000 credits (1,025,151)Woodall LLR Silver: Earned 100,000 credits (123,136)321 Sieve Bronze: Earned 10,000 credits (20,061)Cullen/Woodall Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,074,349)Generalized Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (167,039)PPS Sieve Sapphire: Earned 20,000,000 credits (45,234,841)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Silver: Earned 100,000 credits (108,377)TRP Sieve (suspended) Silver: Earned 100,000 credits (100,605)AP 26/27 Amethyst: Earned 1,000,000 credits (1,115,868)GFN Jade: Earned 10,000,000 credits (14,691,481)PSA Jade: Earned 10,000,000 credits (18,340,315)
Message 49255 - Posted: 9 Feb 2012 | 14:09:56 UTC - in response to Message 44771.

I just found 2175*2^749073+1 is prime.

Is there any way to figure out more properties of this prime?

    Twin Prime? (probably not)


The prime was not tested for twin. You can manually do this by testing the -1 form. In this case, 2175*2^749073-1.



John,

Are you saying that this instance was not tested in the "-1" form to test for a twin due to mistake, or are you saying that all BOINC proth primes are not tested for a twin on the server, just GFN testing?

With the shear number of proth primes being found, does there not exist the possibility that a twin exists???

Neo
AtP

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Found 1 prime in the 2020 Tour de Primes321 LLR Silver: Earned 100,000 credits (154,337)Cullen LLR Bronze: Earned 10,000 credits (65,587)ESP LLR Bronze: Earned 10,000 credits (66,542)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (72,412)PPS LLR Ruby: Earned 2,000,000 credits (4,127,864)PSP LLR Silver: Earned 100,000 credits (104,595)SoB LLR Silver: Earned 100,000 credits (126,157)SR5 LLR Silver: Earned 100,000 credits (161,281)SGS LLR Silver: Earned 100,000 credits (436,634)TRP LLR Gold: Earned 500,000 credits (639,881)Woodall LLR Silver: Earned 100,000 credits (115,733)321 Sieve Bronze: Earned 10,000 credits (10,368)PPS Sieve Ruby: Earned 2,000,000 credits (2,119,298)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (10,227)TRP Sieve (suspended) Bronze: Earned 10,000 credits (21,181)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Turquoise: Earned 5,000,000 credits (8,104,346)PSA Jade: Earned 10,000,000 credits (10,617,327)
Message 49257 - Posted: 9 Feb 2012 | 14:24:39 UTC - in response to Message 49255.

If k (in your case 2175) is divisible by 3 then yes, the possibility of that p-2 is prime exists, i don't know why we don't test those numbers, but as John said, you can test that manually using LLR...

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321 LLR Bronze: Earned 10,000 credits (11,773)Cullen LLR Bronze: Earned 10,000 credits (14,945)ESP LLR Bronze: Earned 10,000 credits (26,855)PPS LLR Bronze: Earned 10,000 credits (84,876)PSP LLR Bronze: Earned 10,000 credits (15,311)SoB LLR Bronze: Earned 10,000 credits (21,440)SR5 LLR Bronze: Earned 10,000 credits (29,270)SGS LLR Bronze: Earned 10,000 credits (26,616)TPS LLR (retired) Bronze: Earned 10,000 credits (36,288)TRP LLR Bronze: Earned 10,000 credits (41,655)Woodall LLR Bronze: Earned 10,000 credits (15,807)321 Sieve Bronze: Earned 10,000 credits (20,014)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (23,405)PPS Sieve Bronze: Earned 10,000 credits (36,192)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (20,306)TRP Sieve (suspended) Bronze: Earned 10,000 credits (21,738)GFN Bronze: Earned 10,000 credits (86,217)PSA Ruby: Earned 2,000,000 credits (2,143,756)
Message 49260 - Posted: 9 Feb 2012 | 14:32:08 UTC - in response to Message 49255.

I just found 2175*2^749073+1 is prime.

Is there any way to figure out more properties of this prime?

    Twin Prime? (probably not)


The prime was not tested for twin. You can manually do this by testing the -1 form. In this case, 2175*2^749073-1.

Are you saying that this instance was not tested in the "-1" form to test for a twin due to mistake, or are you saying that all BOINC proth primes are not tested for a twin on the server, just GFN testing?

With the shear number of proth primes being found, does there not exist the possibility that a twin exists???

No mistake. We do not test proth primes for twins. They are only tested further for xGFN divisibilities.

Yes, there's always a possibility that a twin exists...or a Sophie Germain...or other forms. :) The data set was sieved for single forms on the +1 side so no further candidates were removed due to other forms. NOTE: You stand a much better chance at finding twins by actually sieving for them and then testing a more appropriate data set.

There have been efforts in the past by others to test all the primes in the Top 5000 list for twins. So far, no success. However, the possibility still exists.
____________

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