PrimeGrid’sAP27 Search
On 3 November 2016, 23:35:42 UTC, PrimeGrid’s AP27 Search (Arithmetic Progressionof 27 primes) found the progression of 26 primes:149836681069944461+7725290*23#*n for n=0..25
The discovery was made by Takeshi Nakamura of Japan using a NVIDIA GTX 1070 onan Intel(R) Xeon(R) E5-2667 v3 @ 3.20GHz with 16GB RAM, running Windows 10 Corex64 Edition. This computer took about 30 minutes to process the task (each task tests
100 progression differences of 10 shifts each). Takeshi is a member of theBOINC@MIXI team.
The progression was verified on 4 November 2016 03:37:51 UTC, by James Nobis ofthe United States using an AMD Tahiti GPU on an AMD Opteron(tm) 3648 CPU runningLinux. This computer took about 1 hour 21 minutes to process the task. James is amember of the Sicituradastra. team.
The AP26 will be listed in Jens Kruse Andersen's “Primes in Arithmetic Progression
Records” page (http://primerecords.dk/aprecords.htm) under the section(s):•All known AP24 to AP26 (http://primerecords.dk/aprecords.htm#ap24)

Credits for the discovery are as follows:
1. Takeshi Nakamura (Japan), discoverer
2. PrimeGrid, et al.
3. AP26, a primality program originally developed by Jaroslaw Wroblewski, adapted
to BOINC by Geoff Reynolds with maintenance and improvements by Bryan Littleand Iain Bethune.
Using a single PC would have taken decades to find this progression, so this timely
discovery would not have been possible without the thousands of volunteers whocontributed their spare CPU (and GPU) cycles. A special thanks to everyone who
contributed their advice and/or computing power to the search.
Additional AP Information
How to search for 26 primes in arithmetic progression? by Jaroslaw Wroblewski
http://www.math.uni.wroc.pl/~jwr/AP26/AP26v3.pdf
Primes in arithmetic progression - Wikipedia
https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression
Prime Arithmetic Progression - Wolfram MathWorld
http://mathworld.wolfram.com/PrimeArithmeticProgression.html
arithmetic sequence - The Prime Glossary at the Prime Pages
http://primes.utm.edu/glossary/page.php?sort=ArithmeticSequencePrimeGrid’s
AP27 Search
The 26 terms of the AP26
149836681069944461+7725290*23#*n for n=0..25
23#=2*3*5*7*11*13*17*19*23=223092870
149836681069944461+7725290*223092870*0=149836681069944461
149836681069944461+7725290*223092870*1=151560138187626761
149836681069944461+7725290*223092870*2=153283595305309061
149836681069944461+7725290*223092870*3=155007052422991361
149836681069944461+7725290*223092870*4=156730509540673661
149836681069944461+7725290*223092870*5=158453966658355961
149836681069944461+7725290*223092870*6=160177423776038261
149836681069944461+7725290*223092870*7=161900880893720561
149836681069944461+7725290*223092870*8=163624338011402861
149836681069944461+7725290*223092870*9=165347795129085161
149836681069944461+7725290*223092870*10=167071252246767461
149836681069944461+7725290*223092870*11=168794709364449761
149836681069944461+7725290*223092870*12=170518166482132061
149836681069944461+7725290*223092870*13=172241623599814361
149836681069944461+7725290*223092870*14=173965080717496661
149836681069944461+7725290*223092870*15=175688537835178961
149836681069944461+7725290*223092870*16=177411994952861261
149836681069944461+7725290*223092870*17=179135452070543561
149836681069944461+7725290*223092870*18=180858909188225861
149836681069944461+7725290*223092870*19=182582366305908161
149836681069944461+7725290*223092870*20=184305823423590461
149836681069944461+7725290*223092870*21=186029280541272761
149836681069944461+7725290*223092870*22=187752737658955061
149836681069944461+7725290*223092870*23=189476194776637361
149836681069944461+7725290*223092870*24=191199651894319661
149836681069944461+7725290*223092870*25=192923109012001961

PrimeGrid’s
AP27 Search
About PrimeGrid
PrimeGrid is a distributed computing project, developed by Rytis Slatkevičius and currently
administered by Iain Bethune, James Breslin, Scott Brown, Ulrich Fries, Charley Gielkens,
Michael Goetz, Roger Karpin, Rytis Slatkevičius, and Van Zimmerman.
PrimeGrid is hosted by Rackspace, and their generous contributions have helped make thisproject possible.
PrimeGrid utilizes BOINC and PRPNet to search for primes with the primary goal of bringing theexcitement of prime finding to the "everyday" computer user. Simply download the software andlet your computer do the rest. Participants can choose from a variety of prime forms to search.
With a little patience, you may find a large or even record breaking prime.
BOINC
The Berkeley Open Infrastructure for Network Computing (BOINC) is a software platform
for distributed computing using volunteered computer resources. It allows users toparticipate in multiple distributed computing projects through a single program. Currently
BOINC is being developed by a team based at the University of California, Berkeley led byDavid Anderson.
This platform currently supports projects from biology to math to astronomy. For more
information, please visit BOINC: http://boinc.berkeley.edu
PRPNet
PRPNet is a client/server application written by Mark Rodenkirch that is specificallydesigned to help find prime numbers of various forms. It is easily ported between various
OS/hardware combinations. PRPNet does not run each PRP test itself, but relies on helper
programs, such as LLR, PFGW, phrot, wwww, and genefer to do the work.
For more information, please visit PrimeGrid’s PRPNet forum thread:
http://www.primegrid.com/forum_thread.php?id=1215
For more information about PrimeGrid and a complete list of available prime search projects,
please visit: http://www.primegrid.com