Problems & Puzzles: Puzzles

 Puzzle 794. Prime Generalized Palindromes José de Jesús Camacho sent the following nice puzzle. For sure you know the "generalized palindromes" concept. This type of numbers are the concatenation of nk integer numbers according to the following scheme: GP = n1, n2, ..., nk, nk, ..., n2, n1 One special concatenation arises when n1 to nk are precisely the natural numbers 1, 2, ... nk Two cases are know to be prime numbers a) when nk=1, then GP=11 b) when nk=10, then GP=1234567891010987654321 Q. Find the next prime example?

Contribution came from Shyam Sunder Gupta.

***

Shyam wrote:

Apart from what is known earlier i.e. GP =11 and 1234567891010987654321, there are no other primes up to nk= 11000 i.e. the next prime number will be of more than 88000 digits long.

...

On another issue, I may add that a sequence of another kind of Generalized palindromes exist according to the following scheme: GP1 = n1, n2, n3, -----, nk-1,nk,nk-1,-----n3,n2,n1

For the special case of n1 to nk being natural numbers, the sequence becomes as under: 1,121,12321,----(OEIS A173426)

In this sequence of Generalize palindromes, one prime i.e. for nk=10 and GP1=12345678910987654321 is already known.

I have found a new 17350 digit Prime In the sequence of numbers 1,121,12321,1234321,123454321...( OEIS A173426 ), This prime is obtained for n=2446. This can be denoted in short as 1234567..244524462445......765321

Though this prime have not been certified as yet, but I have checked this prime for primality exhaustively including with PrimeQ Mathematica function.

This prime is very interesting and can easily be remembered. I would suggest to name this as a Platinum prime.

There are no other primes up to nk= 11000 i.e. the next prime number will be of more than 88000 digits long.

***

 Records   |  Conjectures  |  Problems  |  Puzzles