An emirp is a prime number that keeps prime if the digits in base $10$ are written down in reverse order. A Proth-prime is a prime number of the form $2^n\cdot k+1$ with positive integers $n,k$ , $k$ odd and $2^n>k$. I tried to combine this and searched for an emirp of the form $$2^{10000}\cdot k+1$$ with positive odd integer $k$. I arrived at the result $$2^{10000}\cdot 9467623+1$$
Questions :
- The reversed number is a probable prime. Is it actually prime ?
- Is this the smallest odd integer $k$ doing the job ?