## Square of the Primes

**Big Thanks to Puzzle GrandMaster Shawn for submitting this!**

*Answers to this challenge can be entered into the section below; submissions will automatically be revealed when time is up!*

Related: Sum of Primes!

UPDATE: will give a bit more time before unmasking answers! So far, Bobo & Hex are in

Bobo The Bear| PUZZLE MASTER | Profile January 16th, 2013 - 12:04 amMy first response (after about 30 minutes effort) is that only A=11 and A=101 will work. In both cases, A^4 is palindromic, meaning the final prime number is A itself. Cannot yet prove this. (BTW: I am going on the assumption that the picture is not meant to imply that A is an 11-digit prime. Although I am curious as to why that image was chosen.)

Hex| PUZZLE MASTER | Profile January 18th, 2013 - 1:50 pmPossible starting numbers: 11 and 101

11^2^2 = 14641

Reverse digits: 14641 -> 14641

sqrt(sqrt(14641)) = 11

101^2^2 = 104060401

Reverse digits: 104060401 -> 104060401

sqrt(sqrt(104060401)) = 101

DanWebb| Profile January 22nd, 2013 - 11:10 amVery difficult problem. How do I see the comments?

Shawn| PUZZLE GRANDMASTER | Profile January 24th, 2013 - 8:19 amYes! Those were the two solutions at which I arrived. I was hoping to find an answer that was not palindromic, which would have been much more interesting, but I reached the limits of Excel without finding such an animal.

This little trick will work with any number of the form “100…001” but, other than 101, no other such numbers are prime (at least not within the limits of my power to discover them).

@Bobo the header image is a oblique nudge toward finding the first answer, 11, and recognizing the doublesquare=palindrome requirement. Plus, it was easy to find on an image search, and the color matches the webpage, so I guess you could call it destiny!

suineg| PUZZLE MASTER | Profile January 24th, 2013 - 8:59 pmJaja, cool I thought it was an eleven digit prime…. thats why I gave up quickly man, the primes doubled squared gives you a 41 to 43 digit number jajajajaja, but cool man.

onfire| Profile January 28th, 2013 - 2:18 am11

Pavlen| Profile January 31st, 2013 - 4:17 amWhy 11 digits? I tried 11 digit binaries, as decimals but could not find yet. Not easy to reverse numbers even in Excel. I could reverse, but have problems to copy then.

MFox| Profile March 6th, 2014 - 12:03 pm(11^2)^2 = 14641, which is a palindrome, so reverse it and take two square roots to get back to 11.