10901 = 5⁵ + 6⁵
Source → WONplate 145
→ A003347 → A074615 → A217845
→ A226814 → A247099 → A250546
→ A228542

The smallest palindromic prime of length 37
is formed with the use of 10901
[1]^^[0]₁₅^^[10901]^^[0]₁₅^^[1]
Source → Palprime Page 1

You need to append 33 nines to 10901 to get a first prime.
[10901][9^^33]
Source → Appending 9s to k.txt

Multiplying palindrome 10901 with palindrome 11 results in a third palindrome
10901 * 11 = 119911
Source → A229805
Multiplying palindrome 10901 with palindrome 1001 results in a third palindrome
10901 * 1001 = 10911901
Source → Ninedigits Page 7

Alexandru Petrescu [ November 1, 2023 ]

delved into the Fibonacci numbers and found 16
non consecutive terms that sums up to 10901.
1, 1, ₂, 3, 5, ₈, 13, 21, ₃₄, 55, 89, 144, 233,
377, 610, 987, 1597, 2584, 4181, ₆₇₆₅, ₁₀₉₄₆, ...
they are marked in darkbrown color.

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PDG inspired by Alexandru found an expression with only 4 Fibonacci terms
10901 = 10946 – 55 + 5 + 5

Alexandru Petrescu [ November 1, 2023 ]

There are 23 palprimes less than 10901, namely
2,3,5,7,11,101,131,151,181,191,313,353,373,
383,727,787,797,919,929,10301,10501 and 10601
Alexandru tried to express 10901 as a sum of different palprimes from this list.
Due to the large gap between 929 and 10301 it's obvious that one of a term
might be 10301, 10501 or 10601.
He obtained a number of such representations having 5, 6, 7, 8 or 9 terms. Exemplification:
10901 = 3 + 5 + 101 + 191 + 10601 (5 terms)
10901 = 3 + 5 + 7 + 11 + 101 + 131 + 151 + 191 + 10301 (9 terms)

Alexandru Petrescu [ November 13, 2023 ]

10901is a semiprime →  11  *  991 
with the following very nice notability
10901 is the sum of  11  consecutive primes,  991  being
the median of this sequence.
In formal notation → prime(162) + prime(163) + ... + prime(171) + prime(172)
or written out
10901 = 953 + 967 + 971 + 977 + 983 +  991  + 997 + 1009 + 1013 + 1019 + 1021

YOUR TURN with 10901