What is the largest palindromic prime which remains prime as the two digits at each end are peeled off, one pair at a time, until only a 3-digit prime is left?

For example, from the palindromic prime 30961016903, peel off the end digits 30 and 03 to get the palindromic prime 9610169, then peel off 96 and 69, to leave the prime 101.