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Michael GoetzVolunteer moderator Project administrator Project scientist
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Yes, we have our first mega prime of the new year.
Details will be forthcoming once the necessary steps are taken. (The double checker needs to report the task as finished, and the prime needs to be reported to the top 5000 list).
This prime will make it into the top 20 on the top 5000 list. Using the rankings on the PG home page, that means it's either 321, Cullen, PSP, SoB, Woodall, GFNShort, or GFNWR. (Saying it's in the top 20 rules out SR5 and TRP, which currently could place as high as 65th and 22nd on the list, respectively.) Let the wild speculation begin! The numbers in all projects except for SGS, PPS, and PPSE have grown so large that they're all searching for mega primes now.
A note to all: It does pay to have your computer set to "report results immediately". In this case, the double checker's computer (which still hasn't officially reported the task as completed) actually completed the calculation first  it uploaded the results to the server about two hours before the official prime finder's computer did. But the prime finder's computer reported the task as completed, and the double checker's computer didn't. That's what counts. (Of course, very few people get to be even a double checker on a mega prime, so that's still quite the accomplishment!)
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I will guess a Woodall, since we have not had one in a while.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Since all of the projects that can produce primes in the top 20 currently will produce nothing smaller than the 12th largest prime ever found, and since the largest prime ever found at PrimeGrid currently holds the #12 spot, I can also say:
This is the largest prime ever found at PrimeGrid!
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HonzaVolunteer moderator Volunteer tester Project scientist Send message
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Hmm, at least 3M digits I would say.
Not SoB since it would be Top10 so other forms are still in play...
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Hmm, at least 3M digits I would say.
Not SoB since it would be Top10 so other forms are still in play...
PSP, GFNShort and GFNWR are also in the top 10.
If it's in the top 10, it will therefore either knock off one of the very few remaining k's in either the Sierpinski Problem or the Prime Sierpinski Problem (either would also be the largest known Proth prime), or it will be the first ever n=21 GFN prime (as well as being the largest known GFN prime), or it will simply be the largest prime number ever discovered.
Otherwise, it will "merely" be the largest prime number PrimeGrid's ever discovered. :)
Whatever it is, it sure is a good way to start off the new year!
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[DPC]CharleyVolunteer moderator Project scientist Send message
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Seeing how there's a challenge on GFN, I'd guess it's one of those. :)
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Ken_g6Volunteer developer
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Details will be forthcoming once the necessary steps are taken. (The double checker needs to report the task as finished, and the prime needs to be reported to the top 5000 list).
Doesn't GFN only produce probable primes? So that a run of PFGW would need to be in this list if it were a GFNShort or GFNWR?
Otherwise, I have a GFNWR that might fit the bill.
I feel like it's been announced that a lottery somewhere won something, but I haven't been able to check my lottery ticket's numbers yet.
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GFN is PRP project, so formally double checking is not enough for reporting the number as a prime :)
The double checker needs to report the task as finished, and the prime needs to be reported to the top 5000 list
Let's look at official annoncement of 475856^524288+1 (GFN)
The discovery was made by Masashi Kumagai of Japan using an NVIDIA GeForce GTS 450 in an AMD FX(tm)8150 CPU with 8GB RAM, running 64 bit Windows 7. This GPU took 7 hours 47 minutes to probable prime (PRP) test with GeneferCUDA. Masashi Kumagai is a member of the Team 2ch team.
The prime was verified by Jason Preszler of the United States using an Intel Core i72600 CPU @ 3.40GHz with 12GB RAM, running 64 bit LINUX . This computer took 46 hours 55 minutes to probable prime (PRP) test with GenefX64. Jason is a member of the Turan@BOINC team.
The PRP was confirmed prime by an Intel Core i7 2600k @ 3.4Ghz with 8 GB RAM, running Windows 7 x64. This computer took 70 hours 48 minutes to complete the primality test using LLRx64.
But I found that 475856^524288+1 was also verified by RedHat Virtual STEM Server:
machine : RedHat Virtual STEM Server
what : prime
notes :
Command: /home/caldwell/client/pfgw t q"475856^524288+1" 2>&1
PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14]
Primality testing 475856^524288+1 [N1, BrillhartLehmerSelfridge]
Running N1 test using base 3
Calling BrillhartLehmerSelfridge with factored part 78.79%
475856^524288+1 is prime! (791256.0528s+0.4319s)
[Elapsed time: 9.16 days]
By such complex reasoning I can imagine that this is not GFN :)
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Doesn't GFN only produce probable primes? So that a run of PFGW would need to be in this list if it were a GFNShort or GFNWR?
By such complex reasoning I can imagine that this is not GFN :)
Your thinking is correct and therefore it can't be a GFN.
Seeing how there's a challenge on GFN, I'd guess it's one of those. :)
I wish it were so. Alas, it's not.
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RogerVolunteer moderator Project administrator Volunteer developer Volunteer tester Project scientist
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I am thinking its 321. We're far into the tail of the probability distribution on that one. 



This is stupendous news, but too bad I have been working on my TRP badge instead of my Cul/Woo/PSP badges. Oh well, if it weren't for all of us that don't find mega primes, it would take much longer for others to find mega primes.
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Judging by the wording of MG's leadoff post, it sounds like the MEGA port on PRPnet is ruled out also. Too bad. :) (tests would produce megaprimes, but are too small for top 20 anyway)
I'll hope for SoB or PSP; I favor the conjecture work.
Congratulations all 'round. Pop open an "adult beverage".
Gary
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87*2^3496188+1 is prime! (1052460 digits)
4 is not prime! (1 digit) 


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I'm going to shoot for k=168451 for the Prime Sierpinski Problem, since this k is trailing behind with about 3000 in the "Maximum n in progress". This could be due to a server glitch or an extremely dry testarea for the PSP conjecture for the given k, however it is my best offer... weather I'm right or wrong will show in the next few days :)
Also given the fact that for most conjectures, primes seem to come rather close to each other and for SOB a prime was found for n=13018586 so this actually opens up for PSP to be likely to prime a k at n~=15326928.
So when all comes to all, most likely candidate is the PSP conjecture.
Now I just have to wait and see if the reasoning actually made me right :)
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Ken_g6Volunteer developer
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So, announcements for two new primes appeared on the homepage, one for TRP and one for SR5. I assume neither is this prime?
Edit: I see they were discovered last year, so they can't be this prime that way too.
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Scott BrownVolunteer moderator Project administrator Volunteer tester Project scientist
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So, announcements for two new primes appeared on the homepage, one for TRP and one for SR5. I assume neither is this prime?
Edit: I see they were discovered last year, so they can't be this prime that way too.
That' correct, neither of these are the 2014 prime, which is actually much bigger than either of these.



Michael GoetzVolunteer moderator Project administrator Project scientist
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Judging by the wording of MG's leadoff post, it sounds like the MEGA port on PRPnet is ruled out also. Too bad. :) (tests would produce megaprimes, but are too small for top 20 anyway)
Gary
Since I mentioned double checking, you can rule out any PRPNet projects capable of producing mega primes, including GFN524288 which could also produce another #12 prime.
It seems I gave away more hints than intended!
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The equation with several unknowns is too complicated for simply solution :))
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93*10^^{1029523}1 REPDIGIT MEGA PRIME :) :) :)
57*2^^{3339932}1 MEGA PRIME :)
10994460^131072+1 GENERALIZED FERMAT :)
31*332^367560+1 CRUS PRIME :)
Proud member of team Aggie The Pew. Go Aggie! 


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In this case, the double checker's computer (which still hasn't officially reported the task as completed) actually completed the calculation first  it uploaded the results to the server about two hours before the official prime finder's computer did. But the prime finder's computer reported the task as completed, and the double checker's computer didn't.
Has this happened yet? 


Michael GoetzVolunteer moderator Project administrator Project scientist
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In this case, the double checker's computer (which still hasn't officially reported the task as completed) actually completed the calculation first  it uploaded the results to the server about two hours before the official prime finder's computer did. But the prime finder's computer reported the task as completed, and the double checker's computer didn't.
Has this happened yet?
Yes.
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When should we expect an announcement?
(I checked my Cullen results of late, alas, not one of them.)
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Michael GoetzVolunteer moderator Project administrator Project scientist
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When should we expect an announcement?
It's hard to say. It will probably be several more days.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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No news on that prime just yet, but it looks like a second mega prime has been found. It's smaller, so there's a good chance we might be able to release information about the second prime before the first.
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[DPC]CharleyVolunteer moderator Project scientist Send message
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Wow, it's raining primes it seems :o If this is indicative for the rest of the year we're in for one heck of a ride! :D :)
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Wow, it's raining primes it seems :o If this is indicative for the rest of the year we're in for one heck of a ride! :D :)
I expect this to be a good year for mega primes because SR5 is just above the 1 million digit threshold. In the year following TRP reaching the million digit threshold, we found 6 TRP mega primes. I wouldn't be surprised if we find that many SR5 primes this year. Maybe even more: there's more SR5 candidates remaining, which means n and the number of digits should advance more slowly than it did with TRP.
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Ken_g6Volunteer developer
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It's smaller, so there's a good chance we might be able to release information about the second prime before the first.
Does that mean that you recheck large primes inhouse before submitting them to the top 5000 list? Or does it mean that you wait for the top 5000 list to verify your large primes before announcing them?
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HonzaVolunteer moderator Volunteer tester Project scientist Send message
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Does that mean that you recheck large primes inhouse before submitting them to the top 5000 list? Or does it mean that you wait for the top 5000 list to verify your large primes before announcing them?
I think the answer is there  http://primes.utm.edu/primes/page.php?id=116922
321 was long overdue, well done.
Previous ones are in Top100 are 7033641, 6090515, 5082306, 4235414, 3136255.
There was none from 8 and 9 millions exponent range.
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Well done PrimeGrid members. 321 crunchers have a great result. Looking forward to one on the minus side ;) 



From the top 5000 list:
12a: 3*2^10829346+1 (3,259,959 digits) L3770 (2014) 



No news on that prime just yet, but it looks like a second mega prime has been found.
So is the 321 prime the second or first mega prime of 2014?
The 321 prime is the largest ever for PrimeGrid. Is there another equally impressive prime number or a smaller mega prime discovery such as another SR5?
It will probably be several more days.
This suggests that the 321 prime isn't the "first" impressive prime of 2014. Perhaps a SoB/PSP prime has been discovered... 


Michael GoetzVolunteer moderator Project administrator Project scientist
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It's smaller, so there's a good chance we might be able to release information about the second prime before the first.
Does that mean that you recheck large primes inhouse before submitting them to the top 5000 list? Or does it mean that you wait for the top 5000 list to verify your large primes before announcing them?
The events that let us publicly announce a prime are usually:
1) We've run the test ourselves to verify the prime. We'll usually run the verification on PFGW to rule out the possibility of an unknown LLR bug producing false prime reports.
2) It's been reported to the top 5K list. It does not need to be listed as 'verified' at the top 5k site before we announce it. If we're confident in the prime and it's recorded at Top 5K, that's sufficient. If the verification is being done internally at Top 5K it can take many days and we don't need to wait. In the case of really large primes, they use "external" verification and use our own verification as proof. That's what was done with this prime.
We also like to have the Fermat Divisor testing done prior to reporting, but in the case of large primes like this one that can take many days and we don't wait. If XGFN divisors are found after the entry is made in the top 5K list, we need to add that information later.
When I post a 'teaser' about a prime also follows certain rules.
If it's an LLR prime on a "+1" number, I'll usually tell you about it as soon as we see that one host has reported it as prime. False positives from LLR on "+1" numbers are rare. On the other hand, if it's a "1" number, I'll wait until the wingman verifies it or we verify it ourselves. On "1" numbers, a typical overclocking error is to erroneously report the number as prime. We get a lot of false primes on "1" LLR tests. We're very skeptical when only one host reports a "1" number as prime and so we wait for the wingman or test it ourselves.
For GFNs, even though there's a lot of overclocking errors, the error doesn't produce false prime reports, so if we see a single GFN prime report from one host there's a very good chance it's really a prime.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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No news on that prime just yet, but it looks like a second mega prime has been found.
So is the 321 prime the second or first mega prime of 2014?
The 321 prime is the largest ever for PrimeGrid. Is there another equally impressive prime number or a smaller mega prime discovery such as another SR5?
It will probably be several more days.
This suggests that the 321 prime isn't the "first" impressive prime of 2014. Perhaps a SoB/PSP prime has been discovered...
The 321 is the first prime. 12th largest known prime, largest 321 prime, and the largest prime found so far at PrimeGrid.
The other prime, which is smaller, is waiting on the wingman. That makes it BOINC, and 'smaller' makes it TRP or SR5. Given what I said in the previous post about "+1" and "1", that would limit it to an SR5 Sierpinski (+1) number.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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The second prime is an SR5: http://primes.utm.edu/primes/page.php?id=116924, and comes in at 66 on the Top 5000 list.
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Very excellent news! The more SR5s we knock out now, the more time we save crunching later (I know we have no control over the distribution of them, but it is nice).
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...We also like to have the Fermat Divisor testing done prior to reporting, but in the case of large primes like this one that can take many days and we don't wait. If XGFN divisors are found after the entry is made in the top 5K list, we need to add that information later.
I can share the following timesaving feature for this stage.
(It can be found by examining the PFGW source. The gos# option, and/or the xgos{#,#} option)
In the interest of time, for the very large Proth primes, you can deserialize the (x)GF test by launching many individual tests in parallel:
#!/bin/csh f
foreach i (2 3 5 6 10 12)
nohup pfgw gos$i lgos$i.log p >& verb_gos$i.log &
end
These tests will return the answer immediately, as soon as done squaring in the given base. xGF can be similarly split but it is usually of less interest  and can be left running as is (with simple gxo).
For even larger Proth primes (one day, this will happen), you may want to build a slightly modified prime95 and use it in PRP test mode with # squaring iterations changed to the Proth's n (thus, it will become the GFdivisor test) and the residue value checked for the last 50 iterations against 1 and 1 (with 1, you can exit); this binary can be used to run with 16 (or, say, 12) threads on a decent ECCcapable multicore Xeon (e.g.), with "base" value controlled from prime.txt and WorkerThreads=16 in local.txt. This will be almost an order of magnitude faster still per each GF(b) test. Furthermore, the residues for the last 50 iterations can be of course saved as well and combined by an external simple program  this will amount to reenginering the PFGW internals, but WorkerThreads times faster.
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P.S. I've run the modified P95 and I have full residues from iteration 10829300 in a few prime bases.
For base 2, the final iterations are:
3*2^10829346+1 interim We8 residue 8BB12511EBCA6473 at iteration 10829338
3*2^10829346+1 interim We8 residue F3F706D81ACDF7DB at iteration 10829339
3*2^10829346+1 interim We8 residue F6AE79E4BD60DC32 at iteration 10829340
3*2^10829346+1 interim We8 residue EC54319B2C948957 at iteration 10829341
3*2^10829346+1 interim We8 residue 78B9B82A62E4A836 at iteration 10829342
3*2^10829346+1 interim We8 residue 9623E426427DD4AD at iteration 10829343
3*2^10829346+1 interim We8 residue 0000000000000001 at iteration 10829344
3*2^10829346+1 interim We8 residue 0000000000000000 at iteration 10829345
3*2^10829346+1 interim We8 residue 0000000000000000 at iteration 10829346
Note: 0000000000000001 is not 1(mod p), neither is 0000000000000000 a zero. These are just last 64bits of residue.
A successful test would have shown a 0000000000000000 64bit residue before the 1 (mod p). I.e. a lucky residue would have been = k*2^n = 1 (mod p), followed by the string of 1 (mod p) for the rest of the run.
TL;DR version of the above. This is not a Fermat divisor, unfortunately. 



3*2^10829346+1 is not a Fermat divisor, unfortunately.
A prime of the form 3*2^n+1, where n is even, cannot be a factor of any Fermat number.
See http://www.ams.org/journals/proc/195800905/S00029939195800966147/
Yves 



You are absolutely right, Yves, and (unsurprisingly) the last (fulllength) residues base 2 are indeed of the Robinson's form (as shown on the last page of the paper).
However, the good news are that this number divides:
GF(10829343,3)
GF(10829345,5)
GF(10829345,11)
some composite base GFNs (6? 10?*) and undoubtedly many xGFs.
(I was away for the whole day and only saw one run finish, not the other bases. It was a proof of concept set of P95 runs, so let's just wait for the official report for the gxo results.)
______________
* needed residues base 2 for these. 6=2*3, 10=... etc 



Very excellent news! The more SR5s we knock out now, the more time we save crunching later (I know we have no control over the distribution of them, but it is nice).
Nice for some!  but, alas, this means my time at the top of the SR5 'heap' was tragically short... but sweet nonetheless!
Congrats to Raymond  our new SR5 recordholder!
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For those wondering about these announcements:
The new SR5 announcement is now up and the news posted.
I am still waiting on the divisor testing to be completed before posting the 321 find announcement.




It is interesting that out of 48 known Proth primes with k=3 and n>1, 40 divide GF(•,3) (including the last one).
The 48 primes are in two classes n mod 3:
• 3n (majority, 35 of them, and all divide GF(•,3) *) and
• n=3k+2 (minority, 13 of them; 5 divide and 8 don't: with n= 2, 5, 8, 353, 2816, 20909, 42665, 362765). This is roughly 1/k as expected.
This is similar to divisibility of F(), but the "luck" is in reverse.
The 48 primes are in two classes n mod 2:
• even (majority, 28 of them, and none divide F() /by Morehead Thm./) and
• odd (minority, 20 of them; of which 8 divide). This is roughly 1/k as expected.
________________
*There is a probably rather simple proof out there, too? A la Morehead/Suyama?




• 3n (majority, 35 of them, and all divide GF(•,3) *) and
________________
*There is a probably rather simple proof out there, too?
You may read
A note on factors of generalized Fermat numbers. Ismael Jiménez Calvo, 2000.
Yves 



Thanks! I wonder if Mark would implement these in pfgw. 



A note to all: It does pay to have your computer set to "report results immediately". In this case, the double checker's computer (which still hasn't officially reported the task as completed) actually completed the calculation first  it uploaded the results to the server about two hours before the official prime finder's computer did. But the prime finder's computer reported the task as completed, and the double checker's computer didn't. That's what counts. (Of course, very few people get to be even a double checker on a mega prime, so that's still quite the accomplishment!)
Is there a way to set this in BOINC? cant seem to find it.
One of my computers seems to be doing it all of a sudden but I would like to set that to report right away on all my computers.



Michael GoetzVolunteer moderator Project administrator Project scientist
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A note to all: It does pay to have your computer set to "report results immediately". In this case, the double checker's computer (which still hasn't officially reported the task as completed) actually completed the calculation first  it uploaded the results to the server about two hours before the official prime finder's computer did. But the prime finder's computer reported the task as completed, and the double checker's computer didn't. That's what counts. (Of course, very few people get to be even a double checker on a mega prime, so that's still quite the accomplishment!)
Is there a way to set this in BOINC? cant seem to find it.
One of my computers seems to be doing it all of a sudden but I would like to set that to report right away on all my computers.
You have to set it up in cc_config.xml.
That being said, we recently discovered that there's a way for us to force this to happen from the server side. We've turned that on, so for most (not all) tasks this will be the norm at PrimeGrid from now on.
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That being said, we recently discovered that there's a way for us to force this to happen from the server side. We've turned that on, so for most (not all) tasks this will be the norm at PrimeGrid from now on.
I love you. 


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+1 


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Aaahhh. 

