[seqfan] Kind of truncatable sequence

[Eric Angelini]

Hello SeqFans,

In reading A024770 (Right-truncatable primes: every
prefix is prime)...
[http://www.research.att.com/~njas/sequences/A024770]

... I've had the idea of an monotonically increasing
sequence S like this:

S = 2,3,5,7,29,31,59,71,293,313,593,719,2939,3137,5939,
7193,29399,31379,59393,71933,293999,313797,593933,719333,
2939999,3137977,5939333.

... which is finite and stops there.

Definition: "Erase the last digit of every prime of S;
the result reproduces S without it's last terms"

We know that this kind of sequence is finite, as the
biggest right-truncatable prime is 73939133.

Question:

What could be the longest such sequence (in term of
quantity of integers)?

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P.-S.
One could see the above sequence of primes like this:

S = 2,      3,      5,      7,
    29,     31,     59,     71,
    293,    313,    593,    719,
    2939,   3137,   5939,   7193,
    29399,  31379,  59393,  71933,
    293999, 313797, 593933, 719333,
    2939999,3137977,5939333  STOP

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