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Type of prime?
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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?
____________
Proud member of Team Aggie the Pew
"Wir mÃ¼ssen wissen. Wir werden wissen."
"We must know, we shall know."
 David Hilbert, 1930
 

Michael GoetzVolunteer moderator Project administrator
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Joined: 21 Jan 10 Posts: 13398 ID: 53948 Credit: 229,092,028 RAC: 149,404

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^n1. 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^n1) 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^n1. 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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My lucky number is 75898^{524288}+1  


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."  

JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2875 ID: 2449 Credit: 2,681,934 RAC: 0

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*2^7490731.
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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.
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Michael GoetzVolunteer moderator Project administrator
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Joined: 21 Jan 10 Posts: 13398 ID: 53948 Credit: 229,092,028 RAC: 149,404

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 75898^{524288}+1  

JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2875 ID: 2449 Credit: 2,681,934 RAC: 0

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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NeoVolunteer tester
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Joined: 28 Oct 10 Posts: 710 ID: 71509 Credit: 91,178,992 RAC: 0

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*2^7490731.
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  


If k (in your case 2175) is divisible by 3 then yes, the possibility of that p2 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...  

JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2875 ID: 2449 Credit: 2,681,934 RAC: 0

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*2^7490731.
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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