20141114, 23:32  #1 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9128_{10} 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 supermysterious 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. 
20141115, 00:16  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}·7·163 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 20141115 at 00:55 
20141115, 02:08  #3 
Dec 2012
2×139 Posts 

20141115, 03:01  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}×7×163 Posts 
Ah. Exactly right.

20141115, 03:41  #5 
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 20141115 at 03:53 
20141115, 05:21  #6 
Romulan Interpreter
Jun 2011
Thailand
8873_{10} Posts 
There are 16661 and 19991 with both being prime.
Does it has to have zeroes? 
20141115, 05:35  #7 
Dec 2012
2·139 Posts 
Oh yeah! Thanks LaurV. I did see that one but I forgot about it.

20141115, 06:37  #8 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10001110101000_{2} Posts 
Well, then, allow me to present you with the largest currently known palindrome prime.

20141115, 06:42  #9  
"Tapio Rajala"
Feb 2010
Finland
3^{2}×5×7 Posts 
Quote:


20141115, 09:50  #10 
Romulan Interpreter
Jun 2011
Thailand
19·467 Posts 
Beautiful! Totally!

20141116, 10:28  #11  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23A8_{16} Posts 
Quote:
These constitute a new sequence (the upsidedown 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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