Intereting Posts

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dimension of quotient space
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Prove $∑^{(p−1)/2}_{k=1} \left \lfloor{\frac{2ak}{p}}\right \rfloor \equiv ∑^{(p−1)/2}_{k=1} \left \lfloor{\frac{ak}{p}}\right \rfloor ($mod $2)$
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Simplified l'Hospital: please can you check my proof
Every Hilbert space operator is a combination of projections
Something Isn't Right With My Parking

Can anybody be kind enough to explain what exactly is a super palindrome?

Also consider the following example :

$923456781-123456789=799999992:9=88888888$

- On the distribution of “nice” primes (primes $p$ , such that $\pi(p)$ is prime as well)
- Inequiality on prime gaps
- Using the Euler totient function for a large number
- Is there a sequence of 5 consecutive positive integers such that none are square free?
- Prove that $3^{(q-1)/2} \equiv -1 \pmod q$ then q is prime number.
- What is the distribution of primes modulo $n$?

The largest prime factor of $88888888$ is $137$

$88888888:137=648824:101$ ($101$ being largest prime factor of $648824$) = $6424:73$ ($73$ being largest prime factor of $6424$) this in turn equals to $88$ (a palindrome)

Finally, $88:11$ ($11$ being largest prime factor of 88 and a palindrome) equals to $8$ which is also a palindrome.

Now, given this post and its comments, will it be correct to call $88888888$ a super palindrome?

Can it be possible to call a number a super palindrome if it generates non palindromes along with palindromes, provided the non-palindromes finally generate using the method of division by largest prime factor, a palindrome other than 1?

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Based on the linked post’s definition of super-palindrome:

“I define a super-palindrome as a palindrome which is either 1, or which gives another super-palindrome if divided by its largest prime factor.”

88888888 is not a super palindrome since division by its largest prime factor does not yield another super-palindrome. Also, you ended your algorithm early by stopping at 8 since you can say the largest prime factor of 8 is 2 etc. Your number still seems to exhibit interesting properties however and would certainly warrant more investigation!

For example, any $n$-digit number with all of its digits a single number has the same prime divisors as the other 8 $n$-digit numbers with all their digits the same. Also note that your numbers are nearly symmetric upon division of their largest prime factor. If you provided a more rigorous definition of this, that could be interesting to study.

Just some thoughts.

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