mersenneforum.org > Math Palindromic Primes
 Register FAQ Search Today's Posts Mark Forums Read

 2003-04-12, 17:55 #1 S80780   Jan 2003 far from M40 53 Posts Palindromic Primes Hi, all! When dealing with primes, you often hear about twin primes and the twin prime conjecture. I'd like to know if there is a similar conjecture or even theorem dealing with palindromic primes like e.g. 11, 101, and twin palindromic primes like 13 and 31, 17 and 71 etc. Would it be base-independent? Benjamin Some palindrome stuff
 2003-04-13, 02:41 #2 trif     Aug 2002 2·101 Posts Well, 13 and 31 are 1101 and 11111 in base 2 respectively, so it would certainly be base dependent.
 2003-04-13, 08:34 #3 S80780   Jan 2003 far from M40 53 Posts Not certainly. What I mean is the infinite amount of such primes. Their values would, of course, vary base dependent.
 2003-04-13, 17:25 #4 jocelynl   Sep 2002 2·131 Posts Hi Benjamin, How about base 2. 11 and 13, 23 and 29, 47 and 61, 191 and 253. And non prime 95 and 125. There seems to be one in base 2. formula is x(0)=5 x(n) = x(n-1)*2+1 y(0)=5 y(n)=y(n-1)*2+3 Can anyone extrapolate that when one is not prime then both are not prime?
 2003-04-13, 20:53 #5 jocelynl   Sep 2002 2×131 Posts After more evaluation, if one is not prime then the other one can be prime. So far I found no mersenne prime in that chaine. Can there be a mersenne prime M with N={1,2,3.....} P=(2^N*5+2^N-1) M=2^P-1 Joss
 2003-04-13, 23:49 #6 S80780   Jan 2003 far from M40 7D16 Posts For another question I just found an answer on Chris Caldwell's PrimeGlossary: do all palindromic primes have a p^n number of digits? - No! For base-10, I tested it up to 2^31 - 1, which gave 1, 2, 3, 5 and 7 digits. For twin palindromic primes (BTW, I think 'palindromic prime pair' could be a better name to avoid confusion with palindromic primes that are also prime twins, besides it's a nice anaphora.:)) this isn't the case, either. Counter example: 1009 and 9001. Benjamin P.S.: If I got it right, in Chris Caldwell's PrimeGlossary, they are called 'invertable primes'.

 Similar Threads Thread Thread Starter Forum Replies Last Post carpetpool Miscellaneous Math 3 2017-08-10 13:47 emily Math 34 2017-07-16 18:44 CannOfPrimes No Prime Left Behind 6 2013-09-19 01:49 ET_ Lounge 4 2012-02-21 18:20 troels munkner Miscellaneous Math 4 2006-06-02 08:35

All times are UTC. The time now is 04:28.

Thu Jul 7 04:28:21 UTC 2022 up 84 days, 2:29, 0 users, load averages: 1.17, 1.46, 1.60