This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
8179718 is ok because 181797181, 381797183, 781797187 and 981797189 are primes.
2312 is a term because 123121, 323123, 723127 and 923129 are all primes.
Select[ Range[ 30000 ], PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "1", {1, -1} ] ] ] && PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "3", {1, -1} ] ] ] && PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "7", {1, -1} ] ] ] && PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "9", {1, -1} ] ] ] & ]
enclose[n_]:=Table[FromDigits[Join[{i},IntegerDigits[n],{i}]],{i, {1,3,7,9}}]; Select[Range[30000],AllTrue[enclose[#],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 21 2015 *)
263 is included because 263 is a prime and 32633 (and also 92639) is a prime.
q:= p-> ormap(isprime, map(d-> parse(cat(d, p, d)), [1, 3, 7, 9])): select(q, [ithprime(i)$i=1..67])[]; # Alois P. Heinz, Feb 22 2023
brkQ[p_]:=AnyTrue[Table[FromDigits[Join[{d},IntegerDigits[p],{d}]],{d,{1,3,7,9}}],PrimeQ]; Select[Prime[Range[100]],brkQ]
is(p) = my(d=digits(p)); forstep(k=1, 9, 2, if (isprime(fromdigits(concat(k, concat(d,k)))), return(1))); isok(p) = if (isprime(p), is(p)); \\ Michel Marcus, Feb 20 2023
from sympy import isprime, nextprime
from itertools import islice
def agen(): # generator of terms
p = 2
while True:
sp = str(p)
if any(isprime(int(d+sp+d)) for d in "1379"):
yield p
p = nextprime(p)
print(list(islice(agen(), 57))) # Michael S. Branicky, Feb 20 2023
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