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Proth Prime Search :
Fermat divisors by year
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If you search PrimeGrid primes for Fermat divisors, you get this list (For the oldest two, I found the year on the Top 5000 site):
2018: 0 found
2017: 0 found
2016: 0 found
2015: 1 found (267*2^2662090+1)
2014: 1 found (193*2^3329782+1)
2013: 3 found (2145*2^1099064+1; 57*2^2747499+1; 183*2^1747660+1)
2012: 4 found (1705*2^906110+1; 7905*2^352281+1; 131*2^1494099+1; 329*2^1246017+1)
2011: 5 found (25*2^2141884+1; 4479*2^226618+1; 3771*2^221676+1; 9*2^2543551+1; 7333*2^138560+1)
2010: 0 found
2009: 2 found (659*2^617815+1; 519*2^567235+1)
2008: 1 found (651*2^476632+1)
2007: 1 found (151*2^585044+1)
2006: 0 found
2005: 1 found (27*2^672007+1)
This makes me wonder:
When will PrimeGrid find its next Fermat divisor (apparently its twentieth)?
Is there a good explanation (mathematical and/or technical) why we have seen relatively few Fermat divisors recently, or is that simply a conincidence?
/JeppeSN
 


Is there a good explanation (mathematical and/or technical) why we have seen relatively few Fermat divisors recently, or is that simply a conincidence?
/JeppeSN
The numbers we're testing are a lot bigger and primes are harder to find?
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(I am NOT an administrator anymore, so please don't PM me with questions. I can't help.)  

Scott BrownVolunteer moderator Project administrator Volunteer tester Project scientist
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Joined: 17 Oct 05 Posts: 2033 ID: 1178 Credit: 7,281,246,537 RAC: 3,022,506

Is there a good explanation (mathematical and/or technical) why we have seen relatively few Fermat divisors recently, or is that simply a conincidence?
/JeppeSN
The numbers we're testing are a lot bigger and primes are harder to find?
I would add also the following:
1) in the earlier years, PPSE was largely the only game in town. We have a vastly broader set of subprojects now than in prior years, and this means that a smaller proportion of our efforts are placed in the proth prime projects where we usually find Fermat divisors.
2) Proth primes have been further divided into PPSE, PPS, and PPSmega. Thus, our efforts likely to find divisors are even further diminished as considerable PPS effort is focused on finding a mega prime, which is less likely to yield primes overall than PPSE, and thus, divisors.
 

HonzaVolunteer moderator Volunteer tester Project scientist Send message
Joined: 15 Aug 05 Posts: 1859 ID: 352 Credit: 2,845,419,211 RAC: 1,045,112

Just to revive this thread, it may change this year with Fermat Divisor Prime (DIV) subproject and upcoming challenge.
Or will we come up dry again in 2019?
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Just to revive this thread, it may change this year with Fermat Divisor Prime (DIV) subproject and upcoming challenge.
Or will we come up dry again in 2019?
The DIV subproject was created after this discussion (and other discussion like it) had taken place, I believe.
The chances for a Fermat divisor will be much higher for the last four month of 2019 than they were for, say, the last four months of 2018.
I am quite confident we will find at least one Fermat divisor in the DIV subproject during the twelve months of 2020.
/JeppeSN  


The chances for a Fermat divisor will be much higher for the last four month of 2019 than they were for, say, the last four months of 2018.
I am quite confident we will find at least one Fermat divisor in the DIV subproject during the twelve months of 2020.
Update:
2020: ≥1 found (13*2^5523860+1; any more to come?)
2019: 0 found
/JeppeSN  

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