Problems & Puzzles: Puzzles

Puzzle 404. Σ(x^x), for x=1 to n

Let's call S(n)= Σ(x^x), for x=1 to n.

It's known than S(n) is prime for n=2, 5, 6, 10 & 30. See A073825.

Question: Find larger n values that make S(n) prime.



Contributions came from J. K. Andersen & Shyam Sunder Gupta.


Andersen wrote:

"PrimeForm/GW found no other primes for n < 28000."


Shyam wrote:

"There are no more primes up to 8776 term. Any additional terms are greater than 8776 with the next prime having more than 34607 digits.
Considering prime number theorem, percentage of primes in the range of 10^34606 is very small, so probability of finding a prime is remote."


Records   |  Conjectures  |  Problems  |  Puzzles