There are 43 3-digit prime numbers which, when reversed, also yield a prime number. (Eight of these are actually consecutive primes).

Of the 43, 15 are simply palindromes (e.g. 929), but of the remaining 14 pairs of numbers (called 'emirp's), one pair in particular exhibits two unique characteristics, one of which is rather surprising.

What are the numbers, and what are their unique characteristics?

(In reply to re(4): here are the pairs - thx Charlie by rod hines)

Revisiting Excel shows me that 701 + 107 = 808 and 311 + 113 = 424, both palidromic in totals.

But if subtraction is anything to be gained then 733 - 337 = 396, but then too does 743 - 347!

If Charlie's LEE and EEL is one unique characteristic, then having 3 digits being multiples of 3 is obviously not the other.   BTW, I am assuming that the "interesting pattern" in the comment to which I am responding is the digital sum of 18 for the subtractions I note in my spreadsheet.

No, no further joy :-(

Posted by brianjn on 2009-01-12 22:41:08