Is there a largest "nested" prime number? There are some prime numbers which I will call "nested primes" that have a curious property: if the $n$ digit prime number $p$ is written out in base 10 notation $p=d_1d_2...d_n$, then the nested sequence formed by deleting the last digit one at a time consists entirely of prime numbers.  The definition is best illustrated by an example, for which I will choose the number $3733799$: not only is $3733799$ prime, but so are $\{3,37,373,3733,37337,373379\}$.  See here and here if you want to check.
Question: Does there exist a largest nested prime number, and if so, what is it?

From the comments in OEIS A024770 
Primes in which repeatedly deleting the least significant digit gives a prime at every step until a single digit prime remains. The sequence ends at $a(83) = 73939133.$
