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A051362 Primes remaining prime if any digit is deleted (zeros allowed). 19
23, 37, 53, 73, 113, 131, 137, 173, 179, 197, 311, 317, 431, 617, 719, 1013, 1031, 1097, 1499, 1997, 2239, 2293, 3137, 4019, 4919, 6173, 7019, 7433, 9677, 10193, 10613, 11093, 19973, 23833, 26833, 30011, 37019, 40013, 47933, 73331, 74177 (list; graph; refs; listen; history; text; internal format)
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

T. D. Noe and 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.

MAPLE

P:=proc(q) local a, b, i, ok, n; for n from 1 to q do a:=ithprime(n); b:=0;

ok:=1; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n);

for i from 0 to b-1 do if not isprime(trunc(a/10^(i+1))*10^i+(a mod 10^i))

then ok:=0; break; fi; od; if ok=1 then print(ithprime(n)); fi;

od; end: P(10^6); # Paolo P. Lava, Oct 25 2013

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 = lambda n: filter(is_A051362, range(n))

A051362_list(77777) # Peter Luschny, Jul 17 2014

CROSSREFS

Cf. A034302, A010051, A000040, A034895.

Sequence in context: A063643 A057876 A244282 * A034302 A057878 A019549

Adjacent sequences:  A051359 A051360 A051361 * A051363 A051364 A051365

KEYWORD

nonn,base,nice

AUTHOR

Harvey P. Dale, May 31 2000

STATUS

approved

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Last modified November 28 00:12 EST 2021. Contains 349395 sequences. (Running on oeis4.)