Comments on: Number Theory, Hash Tables, and Geometric Progressions http://www.jakevoytko.com/blog/2007/09/30/number-theory-hash-tables-and-geometric-progressions/ Ye Olde Computer Science Blogge Fri, 18 Jun 2010 17:23:52 +0000 hourly 1 http://wordpress.org/?v=3.0 By: Jake http://www.jakevoytko.com/blog/2007/09/30/number-theory-hash-tables-and-geometric-progressions/comment-page-1/#comment-90 Jake Mon, 01 Oct 2007 23:08:01 +0000 http://www.jakevoytko.com/blog/2007/09/30/number-theory-hash-tables-and-geometric-progressions/#comment-90 http://books.google.com/books?id=-9pg-4Pa19IC&pg=PA476&lpg=PA476&dq=list+of+smallest+primitive+roots&source=web&ots=Aq1PMtxHm_&sig=KCH55f8ODuQ0UjSQRSWAQP2iE3w#PPA606,M1 The above link (page 606) has a list of generators less than 1000, but I'm guessing that you need to find primitive roots of larger primes. This is generally just done through testing. Primes are guaranteed to have phi(phi(p)) primitive roots, and they can generally be found quickly if you can factor phi(p), as I mention above, though I wouldn't recommend using the code in the post, as it doesn't rely on either primality testing or factoring. http://books.google.com/books?id=-9pg-4Pa19IC&pg=PA476&lpg=PA476&dq=list+of+smallest+primitive+roots&source=web&ots=Aq1PMtxHm_&sig=KCH55f8ODuQ0UjSQRSWAQP2iE3w#PPA606,M1

The above link (page 606) has a list of generators less than 1000, but I’m guessing that you need to find primitive roots of larger primes. This is generally just done through testing. Primes are guaranteed to have phi(phi(p)) primitive roots, and they can generally be found quickly if you can factor phi(p), as I mention above, though I wouldn’t recommend using the code in the post, as it doesn’t rely on either primality testing or factoring.

]]> By: cookbook http://www.jakevoytko.com/blog/2007/09/30/number-theory-hash-tables-and-geometric-progressions/comment-page-1/#comment-89 cookbook Mon, 01 Oct 2007 21:12:13 +0000 http://www.jakevoytko.com/blog/2007/09/30/number-theory-hash-tables-and-geometric-progressions/#comment-89 Is there a cookbook of well known generators? This would solve many problems of mine. Is there a cookbook of well known generators? This would solve many problems of mine.

]]> By: Eric Jablow http://www.jakevoytko.com/blog/2007/09/30/number-theory-hash-tables-and-geometric-progressions/comment-page-1/#comment-87 Eric Jablow Mon, 01 Oct 2007 15:45:55 +0000 http://www.jakevoytko.com/blog/2007/09/30/number-theory-hash-tables-and-geometric-progressions/#comment-87 Mersenne primes are primes of the form 2^{p}-1, not 2^{p}+1. Mersenne primes are primes of the form 2^{p}-1, not 2^{p}+1.

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