A056714 Numbers k such that 5*10^k + 3*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 3, 13, 25, 49, 143, 419, 1705, 13993, 35753, 40889

Offset: 1

Author

Robert G. Wilson v, Aug 11 2000

Keywords

• nonn

Comments

Also numbers k such that (16*10^k - 1)/3 is prime.

5*10^a(n) + 3*(10^a(n) - 1)/9 is a solution for part (b) of questions of puzzle 244 from www.primepuzzles.net. If a(n) is greater than 5812 then a(n) is an example that is asked for in this question. - Farideh Firoozbakht, Dec 02 2003

Links

• Makoto Kamada, Prime numbers of the form 533...33.
• Carlos Rivera, Puzzle 244. Null Conjunction, The Prime Puzzles and Problems Connection.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A093674, A350995.

Programs

Mathematica

Do[ If[ PrimeQ[ 5*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 5000}]

Extensions

1705 from Farideh Firoozbakht, Dec 18 2003

13993, 35753 and 40889 from Serge Batalov, Jan 2009 confirmed as next terms by Ray Chandler, Feb 11 2012