OFFSET
1,1
COMMENTS
These might be called "super-prime numbers". - Jaime Gutierrez (jgutierrez(AT)matematicas.net), Sep 27 2007
A proper subset of A034895. - Robert G. Wilson v, Oct 12 2014
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
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..201 (terms < 10^13; first 100 terms from T. D. Noe)
CodeGolf StackExchange, Find largest prime which is still a prime after digit deletion, 2013.
Mathematics StackExchange, Deleting any digit yields a prime, 2011.
Mathematics StackExchange, Largest prime that remains prime when any one of its digits is deleted, 2021.
MATHEMATICA
rpQ[n_]:=Module[{idn=IntegerDigits[n]}, And@@PrimeQ[FromDigits/@ Subsets[ IntegerDigits[ n], {Length[idn]-1}]]]; Select[Prime[Range[40000]], rpQ]
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 *)
PROG
(Haskell)
import Data.List (inits, tails)
a051362 n = a051362_list !! (n-1)
a051362_list = filter p $ drop 4 a000040_list where
p x = all (== 1) $ map (a010051 . read) $
zipWith (++) (inits $ show x) (tail $ tails $ show x)
-- Reinhard Zumkeller, Dec 17 2011, Aug 24 2011
(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
(Sage)
def is_A051362(n):
prime = is_prime(n)
if prime:
L = ZZ(n).digits(10)
for k in range(len(L)):
K = L[:]; del K[k]
prime = is_prime(ZZ(K, base=10))
if not prime: break
return prime
A051362_list(77777) # Peter Luschny, Jul 17 2014
(Python)
from sympy import isprime
def ok(n):
if n < 10 or not isprime(n): return False
s = str(n)
return all(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Nov 02 2023
CROSSREFS
KEYWORD
nonn,base,nice
AUTHOR
Harvey P. Dale, May 31 2000
STATUS
approved