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Lucky Palindromes: when do prime factors of palindromes make palindromes?

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POSTED BY: Vitaliy Kaurov
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POSTED BY: Roman Maeder

Why do you exclude palindromes with a single (multiple) prime factor? they make for some pretty patterns, and in particular, a lucky palindrome that is a square has a prime factor that is itself a palindrome, like this 17 digit example:

12323244744232321 == 111010111 111010111

which is also a double lucky palindrome, of course. There are higher powers, as well:

343 == 7 7 7
14641 == 11 11 11 11
POSTED BY: Roman Maeder

Great question. Because there is no asymmetry. It is easy to get a palindrome from 2 or more identical palindromes. But it is much harder for not-identical non-palindromic factors to line up to form a palindrome. I am just curious about these not-trivial cases, if that makes sense.
POSTED BY: Vitaliy Kaurov
POSTED BY: Vitaliy Kaurov
POSTED BY: Roman Maeder

I actually agree, Roman, single multiple prime factor are also very nice. When you done with your search I'd love to see the sequences complete with those numbers and the optimized code. Thank you very much for looking into this.
POSTED BY: Vitaliy Kaurov
POSTED BY: Roman Maeder

Wow, Roman, great, thank you! It would be really interesting to see the optimized code.

"...no lucky palindromes with 16 digits"

-- do you mean in both ascending and descending order?

294507705507705492 == 223111898111898111322

-- remarkable! And again 5 factors tops - very interesting. I wonder if 7-factors even possible.
POSTED BY: Vitaliy Kaurov

do you mean in both ascending and descending order?

both, I factor the number only once, and then test for both ascending and descending at the same time. They are just a Reverse[] apart.
POSTED BY: Roman Maeder
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