I am searching for a particular type of prime number.
It is of 19 digit.If I removew unit place it will reduce to an 18 digit prime number. If I again remove digit from unit place it will become 17 digit prime number..and so on... What I obtained is each place except first one cannot be filled by even number and $5$. First digit can be filled by $2,3,5$,and $7$ So there are $4.18^4=274877906944$ possible numbers. sum of digits should not be a multiple of $3$.. How to proceed ?
Sequence A024770 in the OEIS has the full list of what are called right-truncatable primes. You can see in the b-file https://oeis.org/A024785/b024785.txt that none have 19 digits.