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A051362
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Primes remaining prime if any digit is deleted (zeros allowed).
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19
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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
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OFFSET
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1,1
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COMMENTS
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These might be called "super-prime numbers". - Jaime Gutierrez (jgutierrez(AT)matematicas.net), Sep 27 2007
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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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)
(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)
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
(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)))
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CROSSREFS
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KEYWORD
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nonn,base,nice
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AUTHOR
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STATUS
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approved
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