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.
(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 |
re: Analytic Solution
