My Math Forum Structure in a class of primes

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July 30th, 2014, 07:00 AM   #11
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Quote:
 Originally Posted by FaustoMorales Could you help me extend my list of base-2 palindromic primes up to 24 bits or so?
The fake primes? This takes it to 25 bits.

Code:
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 July 30th, 2014, 07:23 AM #12 Member   Joined: Aug 2011 Posts: 60 Thanks: 0 I'm sorry if I wasn't clear - I meant real primes... If you could (without too much effort) post the full ordered list of primes that are palindromes when expressed in base 2, say up to 23 or 24 bits, that would really speed up the extension of my exploration of the clustering aspect (I mean questions like: Do the grouping effects keep accentuating as the numbers grow, as it now appears to be the trend?) Last edited by FaustoMorales; July 30th, 2014 at 07:37 AM.
July 30th, 2014, 08:28 PM   #13
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Quote:
 Originally Posted by FaustoMorales I'm sorry if I wasn't clear - I meant real primes... If you could (without too much effort) post the full ordered list of primes that are palindromes when expressed in base 2, say up to 23 or 24 bits, that would really speed up the extension of my exploration of the clustering aspect (I mean questions like: Do the grouping effects keep accentuating as the numbers grow, as it now appears to be the trend?)
I don't think there are any grouping trends, beyond what the palindromes have already (and taking into account that the number of bits must be odd unless the number is 3). But you can find a list of the first 3000 (up to about 29 bits) here:
https://oeis.org/A016041
as recently computed by Michael De Vlieger.

If you need more I'm sure I could go further.

 July 31st, 2014, 04:08 AM #14 Member   Joined: Aug 2011 Posts: 60 Thanks: 0 Thanks for this helpful information - I will report back with more results in a few days. Last edited by FaustoMorales; July 31st, 2014 at 04:15 AM.
 August 2nd, 2014, 05:46 AM #15 Member   Joined: Aug 2011 Posts: 60 Thanks: 0 As far as clustering, further analysis didn't support my initial impresiĆ³n that it was taking place. On the patterns, the peculiar distribution in this sequence of the multiples of primes like 3, 5, and perhaps others, appears to introduce very persistent visual patterns, quite unlike the random increasing sequence, although I can't tell yet whether these patterns tend to strengthen or weaken in general. Fascinating stuff to look at, though!
 August 2nd, 2014, 08:14 AM #16 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms I've heard that science isn't something you do to prove you're right, it's something you do to become right. I guess math is similar. Kudos! Maybe we should make some graphs that are either random (with the right distribution) or actual palprimes and see how well the other can visually distinguish them.
 August 2nd, 2014, 08:38 AM #17 Member   Joined: Aug 2011 Posts: 60 Thanks: 0 Excellent point and great idea. Thanks for your support.
 August 2nd, 2014, 10:17 AM #18 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Again, if there's something I can do to help, let me know.

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