A056721 Numbers k such that 8*10^k-1 is prime.

0, 1, 4, 5, 8, 10, 25, 49, 76, 128, 175, 238, 550, 796, 1219, 2012, 2846, 11336, 21296, 49808, 74318, 236891, 608989, 1652593, 1715905, 1990324, 2045966, 2084563, 5112847

Offset: 1

Author

Robert G. Wilson v, Aug 11 2000

Keywords

• nonn
• hard
• more

Comments

Also numbers n such that 7*10^n + 9*R_n is prime, where R_n = 11...1 is the repunit (A002275) of length n.

Links

• Makoto Kamada, Prime numbers of the form 799...99.
• Index entries for primes involving repunits

Programs

Mathematica

Do[ If[ PrimeQ[ 7*10^n + (10^n-1)], Print[n]], {n, 0, 3000}]

PARI

is(n)=ispseudoprime(8*10^n-1) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(22)-a(23) from Kamada data by Robert Price, Oct 19 2014

a(24)-a(25) from Kamada data by Tyler Busby, Apr 15 2024

Missing terms from Ryan Propper, Jun 02 2025