Problems & Puzzles: Puzzles

Puzzle 979. Primes and sum of repunits Carlos Rivera asks this: If R(n) is a "Repunit" composed of n digits "1" then S(R(n))* = R(1)+R(2)+…R(n) is prime for n=2497 and 3301. Q. Find more n values such that S(R(n)) is prime? ________________ *Perhaps helps this closed form for S(R(n))=(10^(n+1)-9*n-10)/81. Reference,

---

All these contributions came along the week 16-22 Nov 2019 from Oscar Volpatti, Simon Cavegn, Gennady Gusev

***

Oscar wrote:

I checked the repunit sums with length up to 75001 digits, finding no further primes.

***

Simon wrote:

Did not find any. Searched up to n=60192.

***

Gennady wrote:

No other primes S (n) found for n up to 110000.

***

---