Numbers that are both palindromic and prime

I have run many tests on numbers and range of numbers to check for rare qualities, including palindromic and prime. Yes, i know.

I don’t think I have simply check just that they are just both prime and palindromic.

So here it goes, I ran a python program to check for numbers that qualify both as palindromic and prime up to 10 000. The list isn’t that long:

2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929

Look at that list, so pleasent for the eyes.

Are there other hidden qualities there?

The sum of the twenty numbers in the list is 7121, which happens to be a prime number, who knew?

I started to ponder that number, 7121. The digits in 7121 is a also prime numbers: 2 and 7.

1 is not included in the prime number definition. This seem to be because the factorization would not make sense to include a 1 as it doesn’t change anything, so it was excluded.

If I run the Kaprekar’s routine on 7121, i get the following steps:

7211 - 1127 = 6084
8640 - 0468 = 8172
8721 - 1278 = 7443
7443 - 3447 = 3996
9963 - 3699 = 6264
6642 - 2466 = 4176
7641 - 1467 = 6174

It takes seven steps to reach Kaprekar’s constant 6174. Yup, you remembered correctly, 7 is a also a prime number. What a rush!

What is the use of this procedure? Nothing, but I had joy while this lasted.