A125001 - OEIS

%I #23 Feb 26 2024 19:16:52

%S 369293,3823867,5364431,5409259,7904521,8309369,9387527,9510341,

%T 22038829,27195601,28653263,38696543,39091441,39113161,43744697,

%U 45095839,45937109,48296921,48694231,49085093,49106677,50791927

%N Non-insertable primes: primes with property that no matter where you insert (or prepend or append) a digit you get a composite number (except for prepending a zero).

%C Is the sequence infinite? - _Zak Seidov_, Nov 14 2014

%H David W. Wilson and Zak Seidov, <a href="/A125001/b125001.txt">Table of n, a(n) for n = 1..3000</a>

%H Jeremiah T. Southwick, <a href="https://scholarcommons.sc.edu/etd/5879/">Two Inquiries Related to the Digits of Prime Numbers</a>, Ph. D. Dissertation, University of South Carolina (2020).

%e 369293 is a member because all of 1369293, 2369293, 3369293, ..., 3069293, 3169293, ..., 3692930, ..., 3692939 are composite.

%t nipQ[x_]:=Module[{id=IntegerDigits[x],len},len=Length[id];AllTrue[ Select[ Flatten[Table[FromDigits[Insert[id,n,i]],{i,len+1},{n,0,9}],1],#!=x&], CompositeQ]]; Select[ Prime[Range[3050000]],nipQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 12 2018 *)

%o (Python)

%o from sympy import isprime

%o from itertools import islice

%o def ok(n):

%o     if not isprime(n): return False

%o     s = str(n)

%o     for c in "0123456789":

%o         for k in range(len(s)+1):

%o             w = s + c if k == 0 else s[:-k] + c + s[-k:]

%o             if w[0] != "0" and isprime(int(w)): return False

%o     return True

%o print([k for k in range(10**7) if ok(k)]) # _Michael S. Branicky_, Sep 29 2022

%Y Cf. A356557, A357436.

%K nonn,base

%O 1,1

%A _David W. Wilson_, Jan 08 2007