Repunit: R(n) = (10ⁿ−1)/9 = 111...1 (n ones). R(1)=1, R(2)=11, R(3)=111, R(7)=1111111. Repunit primes: R(2)=11, R(19), R(23), R(317), R(1031)... n must be prime for R(n) to be prime. Generalized: R_b(n) = (bⁿ−1)/(b−1).
How to Use
Enter n:
- R(n): The repunit value
- Prime?: Primality test
- Factors: For small n
Repunit Primes
R(n) prime only if n is prime (necessary, not sufficient). Known prime R(n): n = 2, 19, 23, 317, 1031, 49081, 86453, ... Only 8 known! Finding new ones is an active research area.
Generalized Repunits
In base b: R_b(n) = (bⁿ−1)/(b−1). Base 2: Mersenne numbers M(n)=2ⁿ−1. Base 3: (3ⁿ−1)/2. Repunit concept unifies many primality searches.
Step-by-Step Instructions
- 1Enter n.
- 2View R(n).
- 3Check primality.
- 4See factors.
- 5Try other bases.