The Repunit Primes Project 
Theory
A repunit is a number consisting of copies of the single digit 1. Examples of repunit are 11, 1111, 11111. It's like a repeating unit. A repunit prime is a repunit that is also a prime number. The term "repunit" was coined by A. H. Beiler (1966). Such a number depends on the base that you are using. We concentrate on base10 in this website. In this base, repunits have the form:

R_{p}=(10^p1)/9


It is easy to show that if n is divisible by a, then R_{n} is divisible by R_{a}. For example, 9 is divisible by 3, and indeed R_{9} is divisible by R_{3}, in fact, 111111111 = 111 · 1001001. Thus, for R_{n} to be prime, n must necessarily be prime. But it is not sufficient for n to be prime; for example, R_{3} = 111 = 3 · 37 is not prime. 

The factors of repunit numbers Rp, with p prime, are in the form:

factor = 2k * p + 1

It's very easy to
implement a general algorithm to find factors. The following code is written
using a basiclike language:
p=43 
