Let $p_1,p_2,p_3,..$ be the sequence of primes in increasing order ($p_1=2,p_2=3,...$) .Let $x_n$ be given by:
Question: Is it true that $x_n<1$ for every $n\geq 1$ ?
Note: I haven't written a program to check my conjecture for large values of $n$ (since I don't have a suitable software to do so). I only checked it for small $n$ manually. It would be great if someone can check the conjecture first for large values of $n$.