I happen to notice the following interesting property of some of the prime integers: For example, 13 and it's permutation, 31 are primes. 17 and it's permutation 71 are both primes. But not 19 , it's permutation 91 is not a prime. Again, 3313 is prime, and one of it's permutation 3331 is also prime, however, none of the other permutations are prime such as 1333 or 3133.
I am wondering what are the frequency with which the following primes occur? Given a prime number, all the permutations of it's digits are also prime. Now I think it is almost non-existent beyond 2 digits numbers, but I want to know are there other prime numbers with such property?
On the other hand, I believe at least one permutation of the digits of a prime number is also prime will be much more frequent in nature. It would be interesting to find out when this occurs or do they have any special property?
Any thoughts ?
Tribid,
interesting game. Is there a specific question / purpose behind your question? It seems to me that this is not a fundamental property of primes as it is specific to the decimal system. In the dual system for example 13 = 1101, 31 = 11111.
37 and 73, 79 and 97 are other such pairs. Also an interesting prime is 337 whose all permutations 373, 733 are primes. Others are 113, 199.
Tribid,
interesting game. Is there a specific question / purpose behind your question? It seems to me that this is not a fundamental property of primes as it is specific to the decimal system. In the dual system for example 13 = 1101, 31 = 11111.
@Isha. Great thanks....so there does have other primes of those nature. Hmm....i gotta search a bit more. Thanks. Please share your thoughts if you have other ideas if you would like. Thanks once again.
@David, No it was just something I noticed while playing around with some of the prime numbers. Thanks for sharing your thoughts. By the way, can you explain a bit more about why you believe it is specific to the binary system. Thanks once again for taking time to share your thoughts.
@Tribid
What I wanted to say is that your suggestion is specific to the decimal system. I used the binary system as a counter example for the fundamental nature of any relation between any prime numbers given by the permutation of the digits.
i see. Thanks David.
I find it fascinating that certain combinations of digits in (base 10) gives rise to these prime numbers. Now any permutation of these digits are also primes meaning no matter how you place these numbers in the appropriate places (coeff. in the poly. in 10s), it will give rise to such primes. I don't know why, but I find it fascinating. :)
Anyways...thanks once again.
Well..I just found out that these are called Per-mutable primes...and there aren't very many. In fact, there is a wikipedia entry regarding prime numbers. Here is the link http://en.wikipedia.org/wiki/Permutable_prime
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