Truncatable (left and right side; any number of truncated digits allowed) decimal primes,whose sum of digits is square

[Alexander Povolotsky]

Dear SeqFans,

Here are the three terms of the potential sequence of truncatable
(left and right side; any number of truncated digits allowed) decimal
primes, whose sum of digits (in decimal form) is square:

5375937799, 3953759377999393, 9539537593779993937

a(1)=5375937799 because it arises from truncating a(2) and
5 + 3 + 7 + 5 + 9 + 3 + 7 + 7 + 9 + 9  = 64

a(2)=3953759377999393 because it arises from truncating a(3) and
3 + 9 + 5 + 3 + 7 + 5 + 9 + 3 + 7 + 7 + 9 + 9 + 9 + 3 + 9 + 3 = 100

a(3)=9539537593779993937 because
9 + 5 + 3 + 9 + 5 + 3 + 7 + 5 + 9 + 3 + 7 + 7 + 9 + 9 + 9 + 3 + 9 + 3 + 7 = 121

Is this sequence finite (hope not) ?

Are there similar sequences ?

Regards,
Alex