Problems & Puzzles:
Puzzle 794. Prime
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
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
b) when nk=10, then
Find the next prime example?
Contribution came from Shyam Sunder Gupta.
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:
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
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
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.