perplexus.info :: Numbers : An Odd Couple

An Odd Couple (Posted on 2009-01-10)

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?

Submitted by rod hines

Rating: 4.0000 (1 votes)

Solution: (Hide)

The numbers are 113 and 311. Adding the 3 digits of either number in the 14 prime/emirp pairs yields a number of non-prime sums and just 4 different prime sums, 3 of which occur twice (i.e. 13, 17 and 19). Only the digits in this one pair sum to 5. Secondly, the square of one is the exact reverse of the other; that is, 113^2 = 12769 and 311^2 = 96721.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Up this to D3?	brianjn	2009-01-29 23:37:15
Up this to D3?	rod hines	2009-01-13 11:59:55
re(5): here are the pairs - thx Charlie	brianjn	2009-01-12 22:41:08
re(4): here are the pairs - thx Charlie	rod hines	2009-01-12 14:34:44
Something in common	Gamer	2009-01-11 21:50:10
re(3): here are the pairs - thx Charlie	brianjn	2009-01-11 21:46:49
re(2): here are the pairs - thx Charlie	Charlie	2009-01-11 12:14:13
re: here are the pairs - thx Charlie	brianjn	2009-01-11 06:41:25
here are the pairs	Charlie	2009-01-10 14:23:33

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