27121 Prime Search

PrimeGrid and 12121 Search are now collaborating in an effort to find a Mega Prime of the form 121*2^n-1. 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^n-1. 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^n-1
27*2^n+1, 27*2^n-1

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:

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.

Megabit Prime for 12121 Search

On 4 Dec 2009, PrimeGrid, in collaboration with 12121 Search, found a megabit prime: 27*2^1902689-1. 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*2^1108214-1 Arnold Padro
11/01/2005 - 27*2^777992-1 James Burt
7/14/2005 - 27*2^729314-1 William W. Mikrut
3/31/2005 - 27*2^627794-1 Chris Chatfield

Complete list of n in which 27*2^n-1 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
____________

Status Update

Sieving for the 4 forums (121*2^n+1, 121*2^n-1, 27*2^n+1, 27*2^n-1) 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
____________

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]
____________

Congratulations Honza!
____________
There are only 10 kinds of people - those who understand binary and those who don't

Thanks.

Machine (already retired server) was about to be shut-downed for good one the very same day it found the prime!

____________
My stats

Congrats!

btw, PG now has 34 primes at Top100 rank.
____________
My stats

Ditto.

That's a nice find!

Neo
AtP

Congratulations!!!
____________
My lucky number is 75898⁵²⁴²⁸⁸+1