# What is the least prime $p$, such that $[p-1000,p+1000]$ does not contain a prime $\ne p$?

I am looking for the least prime number $p$, such that the interval $[p-1000,p+1000]$ contains no prime except $p$. In other words, the prime nearest to $p$ has a distance $>1000$ to $p$.

I found a table for prime gaps, giving the lower bound $1.6\times 10^{15}$ for $p$. An example for a $p$ satisfying the condition is $10^{99}+1005697$. The neighbour primes are $10^{99}+1004269$ and $10^{99}+1007193$, but this won't be the least example.

I do not know whether a search for such primes has been made, or if the distance to the nearest prime (instead the distance of the next prime) has been studied intensively.

• Does anyone know a good candidate for $p$ ?