A prime number
that has a decimal
(or other base
, of course) representation consisting entirely of 1
's (i.e. is a "repunit
"). Examples are R(2)=11
1's, I hope). Actually, not many such prime
s are known; and it is not known if infinitely many exist
Easy fact about repunit primes
a prime, then R(q
) is not a prime either.
, with a,b
not 1. Then R(a
) and R(b
) both divide
), as can be seen by considering that the codivisor
has decimal representation 1, followed by a
-1 (or b
's, followed by 1, b
111111 is not prime, since it is 111*1001, and also 11*10101.
Note, however, that R(3)=111 itself is not a prime, even though 3 is.