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A051362 Primes remaining prime if any digit is deleted (zeros allowed).

%I A051362 #59 Feb 13 2024 06:57:19
%S A051362 23,37,53,73,113,131,137,173,179,197,311,317,431,617,719,1013,1031,
%T A051362 1097,1499,1997,2239,2293,3137,4019,4919,6173,7019,7433,9677,10193,
%U A051362 10613,11093,19973,23833,26833,30011,37019,40013,47933,73331,74177
%N A051362 Primes remaining prime if any digit is deleted (zeros allowed).
%C A051362 These might be called "super-prime numbers". - Jaime Gutierrez (jgutierrez(AT)matematicas.net), Sep 27 2007
%C A051362 A proper subset of A034895. - _Robert G. Wilson v_, Oct 12 2014
%C A051362 The largest known number in this sequence is a 274-digit prime consisting of 163 4s, followed by 80 0s, followed by 31 1s. See the CodeGolf link. - _Dmitry Kamenetsky_, Feb 26 2021
%H A051362 Giovanni Resta, <a href="/A051362/b051362.txt">Table of n, a(n) for n = 1..201</a> (terms < 10^13; first 100 terms from T. D. Noe)
%H A051362 CodeGolf StackExchange, <a href="https://codegolf.stackexchange.com/questions/10739/find-largest-prime-which-is-still-a-prime-after-digit-deletion">Find largest prime which is still a prime after digit deletion</a>, 2013.
%H A051362 Mathematics StackExchange, <a href="http://math.stackexchange.com/questions/33094">Deleting any digit yields a prime</a>, 2011.
%H A051362 Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/4038896/largest-prime-that-remains-prime-when-any-one-of-its-digits-is-deleted">Largest prime that remains prime when any one of its digits is deleted</a>, 2021.
%t A051362 rpQ[n_]:=Module[{idn=IntegerDigits[n]},And@@PrimeQ[FromDigits/@ Subsets[ IntegerDigits[ n],{Length[idn]-1}]]]; Select[Prime[Range[40000]], rpQ]
%t A051362 prpQ[n_]:=AllTrue[FromDigits/@Table[Delete[IntegerDigits[n],d],{d,IntegerLength[ n]}],PrimeQ]; Select[Prime[Range[7500]],prpQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 27 2020 *)
%o A051362 (Haskell)
%o A051362 import Data.List (inits, tails)
%o A051362 a051362 n = a051362_list !! (n-1)
%o A051362 a051362_list = filter p $ drop 4 a000040_list where
%o A051362    p x = all (== 1) $ map (a010051 . read) $
%o A051362              zipWith (++) (inits $ show x) (tail $ tails $ show x)
%o A051362 -- _Reinhard Zumkeller_, Dec 17 2011, Aug 24 2011
%o A051362 (PARI) is(n)=my(v=Vec(Str(n)),k);for(i=1, #v, k=eval(concat(vecextract(v, 2^#v-1-2^(i-1))));if(!isprime(k),return(0)));isprime(n) \\ _Charles R Greathouse IV_, Oct 05 2011
%o A051362 (Sage)
%o A051362 def is_A051362(n):
%o A051362     prime = is_prime(n)
%o A051362     if prime:
%o A051362         L = ZZ(n).digits(10)
%o A051362         for k in range(len(L)):
%o A051362             K = L[:]; del K[k]
%o A051362             prime = is_prime(ZZ(K, base=10))
%o A051362             if not prime: break
%o A051362     return prime
%o A051362 A051362_list = lambda n: filter(is_A051362, range(n))
%o A051362 A051362_list(77777) # _Peter Luschny_, Jul 17 2014
%o A051362 (Python)
%o A051362 from sympy import isprime
%o A051362 def ok(n):
%o A051362     if n < 10 or not isprime(n): return False
%o A051362     s = str(n)
%o A051362     return all(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))
%o A051362 print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Nov 02 2023
%Y A051362 Cf. A034302, A010051, A000040, A034895.
%K A051362 nonn,base,nice
%O A051362 1,1
%A A051362 _Harvey P. Dale_, May 31 2000