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 2014-11-14, 23:32 #1 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 942210 Posts Palindrome primes (a.k.a. Elementary S03E03 "Just a Regular Irregular") Last night's Elementary was a bit of a disappointment... because on one superficial level, it dealt with ... (gasp) math. Again, I might add. One of the premises (without giving away any clues) was the existence of a super-mysterious devilish prime number that was palindromic, 666 in the middle, bracketed on both sides by a row of zeroes and ones at the ends. Iirc the one they used had thirteen zeroes. Aw, big deal! Puzzle: find more of these. For bonus points, reminds us the fancy name that they used for describing this number. It escapes me.
 2014-11-15, 00:16 #2 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·7·673 Posts I'll start. I spy eight of them, the largest currently being this. Rudolf Ondrejka called these "beastly palindromic primes". Last fiddled with by Batalov on 2014-11-15 at 00:55
 2014-11-15, 02:08 #3 Jayder     Dec 2012 2×139 Posts
 2014-11-15, 03:01 #4 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 942210 Posts Ah. Exactly right.
 2014-11-15, 03:41 #5 Jayder     Dec 2012 2·139 Posts Sorry, I didn't have anything else to add. I won't even try to find another one of these primes, but I do wonder if we can find one of these primes that is also prime when the 6s are 9s (like turning the number 180 degrees). Is that even possible? None of the ones on that list you posted qualify. Last fiddled with by Jayder on 2014-11-15 at 03:53
 2014-11-15, 05:21 #6 LaurV Romulan Interpreter     Jun 2011 Thailand 25×5×59 Posts There are 16661 and 19991 with both being prime. Does it has to have zeroes?
 2014-11-15, 05:35 #7 Jayder     Dec 2012 2·139 Posts Oh yeah! Thanks LaurV. I did see that one but I forgot about it.
 2014-11-15, 06:37 #8 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 223168 Posts Well, then, allow me to present you with the largest currently known palindrome prime.
2014-11-15, 06:42   #9
rajula

"Tapio Rajala"
Feb 2010
Finland

31510 Posts

Quote:
 Originally Posted by Batalov Well, then, allow me to present you with the largest currently known palindrome prime.
Somehow I was expecting this... .

 2014-11-15, 09:50 #10 LaurV Romulan Interpreter     Jun 2011 Thailand 25·5·59 Posts Beautiful! Totally!
2014-11-16, 10:28   #11
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

24CE16 Posts

Quote:
 Originally Posted by Jayder Sorry, I didn't have anything else to add. I won't even try to find another one of these primes, but I do wonder if we can find one of these primes that is also prime when the 6s are 9s (like turning the number 180 degrees). Is that even possible? None of the ones on that list you posted qualify.
Well, why not?

These constitute a new sequence (the upside-down Belphegor's Primes). Pending.

Allow me to present to you the largest currently known palindrome prime. No, it only looks like a tautology; it's not.

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