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A034302
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Zeroless primes that remain prime if any digit is deleted.
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15
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23, 37, 53, 73, 113, 131, 137, 173, 179, 197, 311, 317, 431, 617, 719, 1499, 1997, 2239, 2293, 3137, 4919, 6173, 7433, 9677, 19973, 23833, 26833, 47933, 73331, 74177, 91733, 93491, 94397, 111731, 166931, 333911, 355933, 477797, 477977
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graph;
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listen;
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internal format)
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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rpnzQ[n_]:=Module[{idn=IntegerDigits[n]}, Count[idn, 0]==0 && And@@ PrimeQ[FromDigits/@ Subsets[IntegerDigits[n], {Length[idn]-1}]]]; Select[Prime[Range[40000]], rpnzQ] (* Harvey P. Dale, Mar 24 2011 *)
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PROG
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(Haskell)
import Data.List (inits, tails)
a034302 n = a034302_list !! (n-1)
a034302_list = filter f $ drop 4 a038618_list where
f x = all (== 1) $ map (a010051 . read) $
zipWith (++) (inits $ show x) (tail $ tails $ show x)
(PARI) is(n)=my(d=digits(n), t=2^#d-1); if(vecmin(d)==0, return(0)); for(i=0, #d-1, if(!isprime(fromdigits(vecextract(d, t-2^i))), return(0))); isprime(n) \\ Charles R Greathouse IV, Jun 23 2017
(Python)
from itertools import product
from sympy import isprime
A034302_list, m = [23, 37, 53, 73], 7
for l in range(1, m-1): # generate all terms less than 10^m
for d in product('123456789', repeat=l):
for e in product('1379', repeat=2):
s = ''.join(d+e)
if isprime(int(s)):
for i in range(len(s)):
if not isprime(int(s[:i]+s[i+1:])):
break
else:
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CROSSREFS
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KEYWORD
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base,nonn,nice
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AUTHOR
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STATUS
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approved
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