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Emir P. Prime (Posted on 2007-04-19) Difficulty: 2 of 5

Can you identify the five-digit sphenic palindrome

  • where the sum of its digits is a palindromic prime,
  • where of one its factors is a multi-digit palindromic prime, and
  • the sum of its factors is also a palindromic prime?

Can you identify any other sphenic palindrome that has these characteristics?

A sphenic number is a positive integer and product of three distinct primes.
A palindromic number is a number that is the same when written forwards or backwards.

See The Solution Submitted by Dej Mar    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Analytic Solution | Comment 3 of 4 |
(In reply to Analytic Solution by JayDeeKay)

"Since xyzyx is a prime, x cannot be 0, even or 5, i.e., x is 1 or 3."

xyzyx is not prime--it's sphenic, so the feasible solutions would not be limited to 12521, 13331, 14141, 31313, or 32123, but to any of the palindromes in the left column below (palindromes with digital sum 11). In fact, 20702 and 50105 are sphenic with a palindromic prime factor (11, so it's not 3-digit).

xyzyx         factors
10901         11 991
11711         7 7 239
12521         19 659
13331         13331
14141         79 179
20702         2 11 941
21512         2 2 2 2689
22322         2 11161
23132         2 2 5783
30503         11 47 59
31313         173 181
32123         7 13 353
40304         2 2 2 2 11 229
41114         2 61 337
50105         5 11 911

  Posted by Charlie on 2007-04-19 14:45:34
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