Comments on: Sonnet primeshttp://www.johndcook.com/blog/2011/03/08/sonnet-primes/ Singular Value ConsultingTue, 17 Jan 2017 15:40:48 +0000hourly1By: Limerick primeshttp://www.johndcook.com/blog/2011/03/08/sonnet-primes/comment-page-1/#comment-616674 Wed, 07 Oct 2015 02:10:54 +0000http://www.johndcook.com/blog/?p=7994#comment-616674[…] See the next post for Mathematica code to list all sonnet primes. […] ]]>By: Sonnet primes in Python — The Endeavourhttp://www.johndcook.com/blog/2011/03/08/sonnet-primes/comment-page-1/#comment-8611 Tue, 08 Jan 2013 13:02:06 +0000http://www.johndcook.com/blog/?p=7994#comment-8611[…] while back I wrote about sonnet primes, primes of the form ababcdcdefefgg where the letters a through g represent digits and a is not […] ]]>By: John V.http://www.johndcook.com/blog/2011/03/08/sonnet-primes/comment-page-1/#comment-8610 Wed, 09 Mar 2011 17:18:35 +0000http://www.johndcook.com/blog/?p=7994#comment-8610I bet this is impossible without allowing leading zeros to be part of the pattern — since I seem to recall that the total number of primes with N digits is not between 10^(N-1) and (10^N)-1. ]]>By: John V.http://www.johndcook.com/blog/2011/03/08/sonnet-primes/comment-page-1/#comment-8609 Wed, 09 Mar 2011 17:11:52 +0000http://www.johndcook.com/blog/?p=7994#comment-8609Hey John — here’s a real he-man prime challenge:

Find a non-trivial pattern (p1, p2, … pn) such that the size of the set of primes with that pattern is itself a member of the set!

]]>By: Michael Alberthttp://www.johndcook.com/blog/2011/03/08/sonnet-primes/comment-page-1/#comment-8608 Wed, 09 Mar 2011 03:25:42 +0000http://www.johndcook.com/blog/?p=7994#comment-8608Still obsessed with base 7. All the sonnet numbers are multiples of 6 there, but 204 of them are of the form 6 times a prime. ]]>By: Michael Alberthttp://www.johndcook.com/blog/2011/03/08/sonnet-primes/comment-page-1/#comment-8607 Wed, 09 Mar 2011 02:52:43 +0000http://www.johndcook.com/blog/?p=7994#comment-8607Seemed natural to work in base 7 instead, but of course odd bases are no good. In base 8, there are 1057 solutions, all of which use the digit 0. So, 10 is the first base where there’s a sonnet prime that doesn’t include a 0 digit (and in fact there are 6367 of those. ]]>