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Message boards : Proth Prime Search : Fermat divisors by year

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Message 124298 - Posted: 4 Jan 2019 | 16:27:39 UTC

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

Message 124300 - Posted: 4 Jan 2019 | 16:32:16 UTC - in response to Message 124298.

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?
____________

My lucky number is 75898524288+1

Message 124301 - Posted: 4 Jan 2019 | 16:59:54 UTC - in response to Message 124300.

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 sub-projects 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 PPS-mega. 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.

Message boards : Proth Prime Search : Fermat divisors by year