Saturday, 15 January 2011

Unbelievably Prime-emirP ylbaveilebnU

Where do they find the time? I came across this amazing piece of trivia on a web page called "Futility Closet" by Greg Ross.

3139971973786634711391448651577269485891759419122938744591877656925789747974914319
422889611373939731 is prime, whether it’s spelled forward or backward. Further, if it’s cut into 10 pieces:

through and through - reversible primes

… each row, column, and diagonal is itself a reversible prime.

Discovered by Jens Kruse Andersen.

Now I'm wondering, is it possible to find a four digit prime that might be similarly divided into a 2x2 rectangle with the same row, column and diagonal primeness? Ahh go on, you know you want to.... but share if you find one.

OK, so 13 and 31 are reversible primes, and 1331 is ....crap.. ok your turn.

Nate said...

A four digit prime with this property does not exist. The first and fourth digit would need to be the same if it is reversible, but the first and fourth digits make up one of the diagonals, and if those digits are the same, the diagonals will be divisible by 11 and therefore not prime, unless the number is 1111, in which case the original is not prime.

I'll think about the 9 digit case...

Nate said...

I posted hastily thinking you meant a palindromic number rather than a number which is different but still prime when reversed.

I checked the possibilities for four digit primes and I could find none, but it was a much more roundabout process.

Pat's Blog said...

Nate,
Thanks for the comments. I actually was amazed at how many of the four digit numbers that could be made up of two of the two digit reversible primes were divisible by three.

11, 13/31, 17/71, 37/73, 79/97.. for example 11 with anything except 17/71 is divisible by three no matter how they are arranged. The same is true for 17/71 and any of the other three pairs. so there are not that many to really eliminate.

Steven Colyer said...
This comment has been removed by the author.
Steven Colyer said...

Pat, if it's not too much trouble, could you put a Recent Comments gadget up in your right hand column? It would help loads in saving time for we your readers' checking to see if you gave us feedback on your responses to our comments.

In any event, this 100-digit prime blows my mind! Seriously, who DOES have that kind of time ?!

I linked this post to Chad Orzel of Uncertain Principles at Union College, NY. The specific link and an interesting poll re primes can be found there, http://scienceblogs.com/principles/2011/01/dorky_poll_favorite_prime_numb.php.