GCW Prime Search

What an unprecedented start in PRPNet to the Generalized Cullen/Woodall Prime search. Thank you to everyone for giving this project a tremendous head start.

The objective of the GCW prime search will be to discover primes on bases that have yet to yield a prime. Therefore, it is not for the faint-hearted. :) The original GCW13 search was fortunate enough to find a World Record GW prime: 563528*13^563528-1. Unfortunately, the GC prime has yet to be discovered. However, if/when it is, it will be the first Mega Prime for either GC or GW. Hopefully in the not to distant future, the GC13 search will resume for 1M<n<2M.

The following bases have yet to produce a prime (highlighted ones have been found):

• Woodall b=43, 104 & 121
  
• Cullen b=13, 25, 29, 41, 47, 49, 53, 55, 68, 69, 73, 79, 101, 109, 113, 116 & 121
  

Base 149 is the next primeless base for both GC and GW. NOTE: some bases are not quite ready. They will be added to the server when prepared.

The initial sieve depth of all bases is 1.5T. However, all will be taken deeper as necessary. Lennart primality tested all bases up to n=100K (except GW121 to 50K). As seen below, this was all double check of previous efforts. For many of the bases, we are already at first pass level. If the current rate keeps up for a few days then we may see first pass on almost all bases. Hopefully all this hard work will translate into a few early primes. :)

GCW Stats:

• User Primes
  
• User Stats
  
• Pending Tests
  
• Server Stats
  

Best of Luck to everyone and thank you for participating!

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base, [limit]
Cullen
13, [1000000]
25, [1000000]
29, [1000000]
41, [1000000]
47, [1000000]
49, [1000000]
53, [1000000]
55, [1000000]
69, [1000000]
73, [1000000]
101, [1000000]
109, [1000000]
116, [500000]
121, [200000]

Do we just do a single check in this search, or is there a double check?
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Do we just do a single check in this search, or is there a double check?

The first success!!!

GW121 falls quickly. 94112*121^94112-1 is prime! Found by Dmitry Domanov (unconnected) on 19 May 2010 at 04:45:00 UTC. The prime is 196021 digits and is the sixth largest known generalized Woodall prime.

Base 121 was the next lowest base that had neither a GC or GW prime. That issue has now been resolved. :) We'll continue to search for the GC121 and maybe add base 149, the next lowest base in which there are no known GC and GW primes. (GW [112000]; GC [180000])

Congratulations to Dmitry and to everyone else participating.

NOTE: The description "94112*121^94112-1" was modified to "94112*11^188224-1" at the Prime Pages in accordance with their canonicalization procedures.
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Update

It's been almost a week since the quick success in removing GW121. It gave a little false hope that a few more would be removed by now. However, it's proving to be as tough as we expected. These primeless bases are holding strong.

All bases except GW104 and GC116 have now been added to the server. We expect these to be ready in a week or two. Sieving continues on the other bases with many being at 2T already.

Best of Luck to everyone and thank you for participating!

GCW Stats:

• User Primes
  
• User Stats
  
• Pending Tests
  
• Server Stats
  

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I think I'll receive an email soon ;)
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There are only 10 kinds of people - those who understand binary and those who don't

It seems [SG-SPEG]Puzzle-Peter has found prime in high-weighted GC68!

Congratulations!
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The second success!!!

I should post updates more often if it means finding a prime shortly afterwards. :D

The heavy weight monster GC68 has fallen: 129897*68^129897+1 is prime! Found by Peter Kaiser (Puzzle-Peter) on 25 May 2010 18:16:49 UTC. The prime is 238043 digits and is the fourth largest known generalized Cullen prime.

Congratulations to Peter and to everyone else participating. Now on to the next one!!! :)
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Congratulations Peter :)
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Thanks folks! It's a bit of a joke. During the past months I spent more than 100k CPU hours with dozens of machines on 27121 without finding anything. Then I put 1 Core on PRPnet for a few hours and bang!

OK, who's next?
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There are only 10 kinds of people - those who understand binary and those who don't

OK, who's next?

The third success!!!

...and to answer your question, Peter, it looks like Larry Hays is next. :D

Another heavy weight monster GW104 has fallen: 129840*104^129840-1 is prime! Found by Larry Hays ( Sideshow_Larry) on 26 May 2010 19:25:30 UTC. The prime is 261897 digits and is the second largest known generalized Woodall prime. EDIT: second only to Lennart's 563528*13^563528-1 at a huge 627745 digits.

Congratulations to Larry and to everyone else participating. Next!!! :)
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It looks like we will soon be searching new (higher) bases, if we continue this way!
Well done everyone
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It looks like we will soon be searching new (higher) bases, if we continue this way!
Well done everyone

GC base [testing limit]

• 32 [100000] prime at n=5
  
• 75 [109097] prime at n=2
  
• 106 [95000] prime at n=1, 3
  
• 115 [95000] prime at n=24
  

As can be seen, none are at n + 2 > b. Therefore, these bases should have been included in the original list. The are no immediate plans to add them since there's plenty of work with the current bases. However, sieving will begin so they'll be ready in the future.

Also being sieved is base 149, the next "primeless" base for both GC and GW. Additionally, just for fun, base 3 is being sieved to n=3M as a possible opportunity to find a GCW Mega Prime. And finally, there's still GC13 for 1M<n<2M.

Again, nothing will be added for now...just giving everyone a heads up as to the future direction of the GCW Prime Search. Best of Luck and thank you for participating!

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It's official!

GC13 is complete to n=1M. It's a bitter-sweet achievement. :) Finding the prime would have been a more exciting occasion...especially a GC Mega Prime. Nevertheless, it's a GREAT milestone to reach. GC13 1M<n<2M will return in the future...most likely for a "Friday the 13th" mini Challenge. ;) Until then, let's knock out some of these lower bases.

Thank you to everyone!
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Update

Progress continues to advance quite nicely even with the longer testing times. This is a direct result from the high participation rate. Thanks!!! Now if we could just find another one of those elusive primes.

It's official...the leading edge of the search is in record territory. The next GC prime found will be the largest known.

All of the original bases have now been added to the server. Sieving continues on the other bases.

Best of Luck to everyone and thank you for participating!

GCW Stats:

• User Primes
  
• User Stats
  
• Pending Tests
  
• Server Stats
  

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Port 12004 is down for several hours :-(

Port 12004 is down for several hours :-(

Looks like MiHost recently has found prime for GW43!

Looks like MiHost recently has found prime for GW43!

Looks like MiHost recently has found prime for GW43!

Yes, a new record GW has been found. More info to come. This sure is going to pad MiHost's lead for the green jersey. :D

Port 12004 is down.

seems to me there is a hit after a long period

GCW13 User MiHost has found 2 primes and 0 PRPs, 1 is hidden

That would be a monster prime. If true, that would be for base 113 and around 900,000 decimal digits (calculating off the top of my head).

World Record GC Prime!!!

Finally, GC relinquishes its stubborn hold on primes...and does so in World Record fashion. GC113 has fallen: 427194*113^427194+1

Found by Ricky L Hubbard (MiHost) on 29 Jan 2012 08:10:03 UTC. The prime is 877,069 digits and is the largest known generalized Cullen prime. BTW, Ricky also holds the World Record for generalized Woodalls as well: 404882*43^404882-1

Congratulations to Ricky and to everyone else participating.
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Congrats Ricky!

John, don't forget to remove the other base 113 candidates from the server since we only care about the first one.

Congratulations for Monster prime!

port prpnet.primegrid.com:12004 is down

hope you get it back online before the challenge starts at 03/11/12
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Sysadm@Nbg
my current lucky number: 113856050^65536 + 1
PSA-PRPNet-Stats-URL: http://u-g-f.de/PRPNet/