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?

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*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

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Oscar wrote:

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

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Simon wrote:

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

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Gennady wrote:

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

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