[ February 21, 2000 ]
Arranging all the base b representations of palindrome 31113

Concatenating all the base b representations of palindrome 31113 in an
upward (2⩽b⩽10) and downward (10⩾b⩾2) string produces two genuine primes.

Prime 1 = 3111346610746111564654000131443423132120211120200100111100110001001

Prime 2 = 1111001100010011120200100132120211443423400013156465746114661031113

The following palindrome with this property is 73837.
Both 31113 and 73837 are composite palindromes.

So, who can provide me the first palindromic prime example ?

Twenty two years later [ February, 2022 ] I wrote a Pari/gp program with
the purpose to search for myself that first palindromic prime example.

\\ Patrick De Geest [ GP/PARI CALCULATOR Version 2.11.4 ] February 7, 2022
{
forstep(a=1,oo,2,
	t=digits(a);
	if(Vecrev(t)==t, 
		spup=[]; spdo=[]; marque=0;
		for(i=2,10, spup=concat(spup,digits(a,i));
		  spdo=concat(digits(a,i),spdo) );
		if(isprime(fromdigits(spup)) && isprime(fromdigits(spdo)),
		  marque=1; print(fromdigits(spdo));print(fromdigits(spup));print());
		if(isprime(a)&&marque, print(a," is a palindromic PRIME!"); break());
	);
);
}

On [ February 10, 2022 ] after running the code for a few hours
the following appeared on my screen

98802520889
is a palindromic PRIME!

Prime 1 = 98802520889313021332645134010555147110065263366522 \
11322002453010531043214211320241130001011231030321 \
1001100002011010022011121011100000001000101101101001100111001

Prime 2 = 1011100000001000101101101001100111001100110000201101002201112 \
11300010112310303213104321421132024113220024530105 \
10065263366522134010555147131302133264598802520889

Note that the primes formed by the concatenations
is of palindromic length itself namely 161 !