Same Digits Embedded Palprimes of Lengths 3, 5 and 7

The idea of embedding palindromic prime (palprime) numbers in the form of pyramid or tree is very famous in the literature, where the previous palprime is in the middle of next, and so on. In these situations there is no limit where it ends, because always we find a next palprime containing previous one. In this work, we brought palprimes of lengths 3, 5 and 7 in such a way that pyramids are with same digits as of palprime. In this case, we have total 15 for length 3, 93 for length 5  and 668 for length 7 palprimes.