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 Emir P. Prime (Posted on 2007-04-19)

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)

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 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         factors10901         11 99111711         7 7 23912521         19 65913331         1333114141         79 17920702         2 11 94121512         2 2 2 268922322         2 1116123132         2 2 578330503         11 47 5931313         173 18132123         7 13 35340304         2 2 2 2 11 22941114         2 61 33750105         5 11 911`

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

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