[QUOTE=paulunderwood;509527]The Fibonacci PRPs [URL="https://primes.utm.edu/top20/page.php?id=39"]U(130021) and U(148091)[/URL] are ripe for a multicore Primo proof. Alternatively, there are some smaller Mersenne cofactors that need proofs.
Congrats for your latest quadruplet.[/QUOTE] I'll take on one of the mersenne cofactors; is there a place where some proofs are reserved, or a list of which need primo proofs? 
[QUOTE=VBCurtis;509537]I'll take on one of the mersenne cofactors; is there a place where some proofs are reserved, or a list of which need primo proofs?[/QUOTE]
Those on [URL="http://www.primenumbers.net/prptop/searchform.php?form=%282%5Ep1%29%2Fn&action=Search"]this list[/URL] but not on [URL="https://primes.utm.edu/top20/page.php?id=49"]this one[/URL]. I recommend at least 16 cores :wink: I don't know about coordination. HTH. 
Speaking about primo proofs:
I have a few (4 + 2) candidates of [URL="https://primes.utm.edu/top20/page.php?id=26"]irregular[/URL] and [URL="https://primes.utm.edu/top20/page.php?id=25"]Euler irregular[/URL] primes waiting for a primo primality proof. They are ranging from about 22000 to 29000 digits, but are far beyond my current computing resources. If one of you is (seriously) interested, please drop me a note. 
[QUOTE=Batalov;509446]Speaking of other primes  Peter Kaiser's latest Quad is out there in outer space!
[url]https://primes.utm.edu/top20/page.php?id=55[/url] [B]10,132 digits! [/B] This quad has a remarkably high difficulty level! Congratulations to Peter![/QUOTE] Congratulations. It is truly impressive! Over twice the number of digits than the previous one (5003 digits on March 2016). 
A new Generalized Fermat has been found
2733014[SUP]524288[/SUP] + 1 While not the largest Generalized Fermat it is (by far) the largest prime for [B]2019[/B] with 3'374,655 digits. Congratulations to Yair Givoni and [URL="http://www.planetary.org/"]The Planetary Society.[/URL] 
4 primes in Arithmetic Progresison
2 Sets
Largest examples for an AP4 a) 1027676400 · 60013# + 1 (4th term) 25992 digits b) 1025139165 · 60013# + 1 (4th term) 25992 digits By Ken J. Davis Congratulations! 
new Generalized Woodall
321671*34^3216711 (492638 digits) is the ninth largest known Generalized Woodall prime, and the ninth known prime of the form n*34^n1.

A new Generalized Fermat has been found
2788032[SUP]524288[/SUP] + 1 While not the largest Generalized Fermat it is the largest prime for [B]2019[/B] with 3'379,193 digits. Congratulations to user "Sheep" 
Sexy primes
Congrats to GENERIC for the primes [p,p+6] = (18041#/14*2^390034)±3.
[url]http://primepairs.com/[/url] 
[QUOTE=paulunderwood;514161]Congrats to GENERIC for the primes [p,p+6] = (18041#/14*2^390034)±3.
[url]http://primepairs.com/[/url][/QUOTE] Congrats! However, that's a strange website with weak, incorrect statements. [QUOTE=http://primepairs.com/]...breaking the prior record of 11,593 digits which, according to Wikipedia, had stood for nearly a decade.[/QUOTE] What about 6521953289619 * 2^55555  5 and [URL="https://primes.utm.edu/primes/page.php?id=114018"]6521953289619 * 2^55555 + 1[/URL] (16737d) dated Apr 2013? Should one think that Peter immediately rushes to Wikipedia to update his record for posterity after finding a record? I am sure that he has other better things to do. Or maybe someone else does for him? Also probably not. There is a reason why even school teachers don't give children a grade for a quote from Wiki. Wiki is broadly correct in generalities, and overwhelmingly incorrect in expert details. The algorithm for searching for facts is: start with a general blurp from Wikipedia, continue searching using links and links from links... then you might build some semblance of a current state of the art. 
[QUOTE=Batalov;514163]Congrats! However, that's a strange website with weak, incorrect statements.
What about 6521953289619 * 2^55555  5 and [URL="https://primes.utm.edu/primes/page.php?id=114018"]6521953289619 * 2^55555 + 1[/URL] (16737d) dated Apr 2013? Should one think that Peter immediately rushes to Wikipedia to update his record for posterity after finding a record? I am sure that he has other better things to do. Or maybe someone else does for him? Also probably not. There is a reason why even school teachers don't give children a grade for a quote from Wiki. Wiki is broadly correct in generalities, and overwhelmingly incorrect in expert details. The algorithm for searching for facts is: start with a general blurp from Wikipedia, continue searching using links and links from links... then you might build some semblance of a current state of the art.[/QUOTE] I'd argue Peter's triplet is not so sexy since there is a prime at 6521953289619 * 2^55555  1 :boxer: On the other hand: [QUOTE]Prime pairs with a prime gap of 6 are known as sexy primes (p, p+6). e.g., (5, 11), (7, 13), (11, 17), (13, 19), (17, 23), etc. [/QUOTE] there is a prime between 17 and 23 :down: 
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