TITLE: Prime numbers of the form $(1\times11\times111\times1111\times...)-(1+11+111+1111+...)$
QUESTION [14 upvotes]: Let
$$R(1) = 1-1,$$
$$R(2) = (1\times11) - (1+11),$$
$$R(3) = (1\times11\times111) - (1+11+111),$$ and so on...
$$R(4)=1355297\quad\text{(a prime number!)}$$
$R(4)$ is the only prime I found of such form up to $R(200)$. Are there anymore primes of such form?

REPLY [2 votes]: If another prime of the form $R(n)$ exists, then $n$ must be at least $490$ and $R(n)$ must have more than $100,000$ digits. 
For the following numbers $n\le 1000$, $R(n)$ has no "small" prime factor :
$$[52, 490, 532, 574, 592, 922, 928, 964]$$
$R(1000)$ has already $499,546$ digits. 
It is unlikely that there is another prime $R(n)$ because the sequence grows very fast and the chance that a number with more than $10^5$ digits is prime, is very low. Of course, this is not a proof. 
A proof that there is no other prime should be out of reach. The only chance seems to be : Finding another prime.