Comments on: Sonnet primes http://www.johndcook.com/blog/2011/03/08/sonnet-primes/ John D. Cook Thu, 23 May 2013 10:27:37 +0000 hourly 1 http://wordpress.org/?v=3.5.1 By: Sonnet primes in Python — The Endeavour http://www.johndcook.com/blog/2011/03/08/sonnet-primes/comment-page-1/#comment-8611 Sonnet primes in Python — The Endeavour Tue, 08 Jan 2013 13:02:06 +0000 http://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 John V. Wed, 09 Mar 2011 17:18:35 +0000 http://www.johndcook.com/blog/?p=7994#comment-8610 I 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 John V. Wed, 09 Mar 2011 17:11:52 +0000 http://www.johndcook.com/blog/?p=7994#comment-8609 Hey 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 Albert http://www.johndcook.com/blog/2011/03/08/sonnet-primes/comment-page-1/#comment-8608 Michael Albert Wed, 09 Mar 2011 03:25:42 +0000 http://www.johndcook.com/blog/?p=7994#comment-8608 Still 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 Albert http://www.johndcook.com/blog/2011/03/08/sonnet-primes/comment-page-1/#comment-8607 Michael Albert Wed, 09 Mar 2011 02:52:43 +0000 http://www.johndcook.com/blog/?p=7994#comment-8607 Seemed 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.

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