Primes in arithmetic progression: Difference between revisions

Revision as of 15:44, 11 December 2023

Revision as of 00:11, 26 December 2023

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For prime ''q'', ''q''# denotes the [[primorial]] 2·3·5·7·...·''q''.

{{As of|2019|9}}, the longest known AP-''k'' is an AP-27. Several examples are known for AP-26. The first to be discovered was found on April 12, 2010, by Benoît Perichon on a [[PlayStation 3]] with software by Jarosław Wróblewski and Geoff Reynolds, ported to the PlayStation 3 by Bryan Little, in a distributed [[PrimeGrid]] project:<ref name="APrecords" />

:43142746595714191 + 23681770·23#·''n'', for ''n'' = 0 to 25. (23# = 223092870) {{OEIS|id=A204189}}

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{| class="wikitable"

|+ Largest known CPAP-''k'' {{as of|2022|05|lc=on}},<ref name="CPAPrecords">Jens Kruse Andersen and Norman Luhn, [https://www.pzktupel.de/JensKruseAndersen/CPAP.htm ''The Largest Known CPAP's'']. Retrieved on 2022-12-20.</ref>,<ref name="Chris K. Caldwell">Chris K. Caldwell, [https://primes.utm.edu/top20/page.php?id=13''The Largest Known CPAP's'']. Retrieved on 2021-01-28.</ref>

|-

! ''k'' !! Primes for ''n'' = 0 to ''k''&minus;1 !! Digits !! Year !! Discoverer