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(Python)
from sympy import isprime
from itertools import count, islice, product
def pals(digs):
yield from digs
for d in count(2):
for p in product(digs, repeat=d//2):
left = "".join(p)
for mid in [[""], digs][d%2]:
yield left + mid + left[::-1]
def folds(s): # generator of suffixes of palindromes starting with s
for i in range((len(s)+1)//2, len(s)+1):
for mid in [True, False]:
t = s[:i] + (s[:i-1][::-1] if mid else s[:i][::-1])
if t.startswith(s):
yield t[len(s):]
yield from ("".join(p)+s[::-1] for p in pals("0123456789"))
def agen():
s, seen = "3", {"3"}; yield from [3]
while True:
for t in folds(s):
if len(t) and t[0] != "0" and t not in seen and isprime(int(t)):
break
s += t; seen.add(t); yield int(t)
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