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PrimeGrid partners with 12121 Search
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JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

27121 Prime Search
PrimeGrid and 12121 Search are now collaborating in an effort to find a Mega Prime of the form 121*2^n1. This is very similar to the 321 Prime Search at k=3.
12121 Search was established on 5/24/2004 to search for large primes of the form 121*2^n1. Later (3/1/2005), they added k=27 to their search. Their "short term" goal is to search for n up to 10M. For more information, please visit their site: 12121 Search.
As we did with 321, we are going to test the +1 form of these k's in parallel as well. Therefore, the effort will consist of the following:
121*2^n+1, 121*2^n1
27*2^n+1, 27*2^n1
for n<10M
First order of business is to establish a coordinated sieving effort to bring all forms to the same depth. Here's the current status:
COMPLETED wrote: 121 1 at p=290T for n<10M
121 +1 at p~450T for n<5M and p=1T for 5M<n<10M
27 1 at p=130T for n<10M
27 +1 at p~450T for n<5M and p=1T for 5M<n<10M
We need two efforts but we'll only focus on one right now:
1. Primary focus  27 1 to bring it up to p=290T then combine with 121 to take to 450T
2. 121 & 27 +1 for 5M<n<10M to bring it up to 450T.
Current progress can be found in the manual sieve reservations. To participate, please see 12121 Sieving Reservation.
Second order of business is to primality test 27 1, 27 +1, and 121 +1 up to n~3.7M to combine it with 121 1. Therefore, candidates will be available for testing in PrimeGrid's PRPNet. If you are interested in participating, please see the PRPNet thread. Port 5000 is currently loaded with 27 & 121 +1 for 600K<n<1.7M.
Again, welcome to 27121 Prime Search and the chance of finding another Mega Prime!!! :)
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JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

Megabit Prime for 12121 Search
On 4 Dec 2009, PrimeGrid, in collaboration with 12121 Search, found a megabit prime: 27*2^19026891. The prime is 572,768 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 76th overall.
The discovery was made by Peter Kaiser of Germany using a dual Intel Xeon X5472 @3.0GHz with 16GB RAM. This computer took 59 minutes and 17 seconds to complete the primality test. Peter is a member of the team SETI.Germany.
This is the 63rd overall prime for k=27 and the 5th prime found by the 12121 Search. Other 12121 Search primes for k=27 are:
3/23/2008  27*2^11082141 Arnold Padro
11/01/2005  27*2^7779921 James Burt
7/14/2005  27*2^7293141 William W. Mikrut
3/31/2005  27*2^6277941 Chris Chatfield
Complete list of n in which 27*2^n1 is prime:
1, 2, 4, 5, 8, 10, 14, 28, 37, 38, 70, 121, 122, 160, 170, 253, 329, 362, 454, 485, 500, 574, 892, 962, 1213, 1580, 2642, 2708, 4505, 8152, 11858, 13300, 15041, 16118, 16778, 19069, 22769, 29020, 30298, 30377, 35942, 42817, 42869, 62024, 74629, 90449, 91042, 117901, 128594, 143330, 152530, 157898, 175852, 282700, 340682, 444622, 627794, 729314, 777992, 1108214, 1163629, 1253870, (...) 1902689
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JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

Status Update
Sieving for the 4 forums (121*2^n+1, 121*2^n1, 27*2^n+1, 27*2^n1) for n<10M has reached p=1220T.
There only a few thousands tests remaining below 2M. We hope to have that completed by the end of the year.
Basic Stats: for PRPNet
port 12006: 27121 Server : User
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JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

Megabit Prime for 27121 Search
On 23 Dec 2009, PrimeGrid's PRPNet found a megabit prime: 27*2^2218064+1. The prime is 667,706 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 56th overall.
The discovery was made by Honza Cholt (Honza) of the Czech Republic using a dual Intel Xeon @ 3.06GHz with 4GB RAM. This computer took 2 hours 38 minutes and 59 seconds to complete the primality test. Honza is a member of the team BOINC.SK.
This is the 45th overall prime for k=27 +1 and the 1st found by PrimeGrid. This form has now been searched to n=2M. (x)gfn divisibility testing is currently underway.
Complete list of n in which 27*2^n+1 is prime:
2, 4, 7, 16, 19, 20, 22, 26, 40, 44, 46, 47, 50, 56, 59, 64, 92, 175, 215, 275, 407, 455, 1076, 1090, 3080, 3322, 6419, 7639, 19360, 30500, 38770, 44164, 50696, 114760, 117784, 153847, 160874, 178739, 379880, 405514, 672007, 974752, 1164664, 1476347, 2218064 [2000000]
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Congratulations Honza!
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There are only 10 kinds of people  those who understand binary and those who don't
 


Congrats to Honza and PrimeGrid. That was a nice Christmas present for the project! :)
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HonzaVolunteer moderator Volunteer tester Project scientist Send message
Joined: 15 Aug 05 Posts: 1806 ID: 352 Credit: 2,446,584,571 RAC: 1,440,589

Thanks.
Machine (already retired server) was about to be shutdowned for good one the very same day it found the prime!
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My stats
Badge score: 1*1 + 5*1 + 7*1 + 8*8 + 9*7 + 11*1 + 12*3 = 187  


Congrats@Pooh_Bear_27 for this huge found ranked at 28th overall...
http://primes.utm.edu/primes/page.php?id=105070
Regards Odi
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HonzaVolunteer moderator Volunteer tester Project scientist Send message
Joined: 15 Aug 05 Posts: 1806 ID: 352 Credit: 2,446,584,571 RAC: 1,440,589

Congrats!
btw, PG now has 34 primes at Top100 rank.
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My stats
Badge score: 1*1 + 5*1 + 7*1 + 8*8 + 9*7 + 11*1 + 12*3 = 187  


Thanks everyone. I now have two awesome finds. The largest Twin Prime and now the first 121 since it's been on the PG project.  

NeoVolunteer tester
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Joined: 28 Oct 10 Posts: 710 ID: 71509 Credit: 91,178,992 RAC: 4,507

Ditto.
That's a nice find!
Neo
AtP  

Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 12516 ID: 53948 Credit: 181,784,294 RAC: 113,058

Congratulations!!!
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Please do not PM me with support questions. Ask on the forums instead. Thank you!
My lucky number is 75898^{524288}+1  


Now hopefully the next 121 is not 6 years away.
Ni
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