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A125001
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Non-insertable primes: primes with property that no matter where you insert (or prepend or append) a digit you get a composite number (except for prepending a zero).
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4
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369293, 3823867, 5364431, 5409259, 7904521, 8309369, 9387527, 9510341, 22038829, 27195601, 28653263, 38696543, 39091441, 39113161, 43744697, 45095839, 45937109, 48296921, 48694231, 49085093, 49106677, 50791927
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internal format)
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OFFSET
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1,1
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COMMENTS
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Is the sequence infinite? - Zak Seidov, Nov 14 2014
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LINKS
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EXAMPLE
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369293 is a member because all of 1369293, 2369293, 3369293, ..., 3069293, 3169293, ..., 3692930, ..., 3692939 are composite.
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MATHEMATICA
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nipQ[x_]:=Module[{id=IntegerDigits[x], len}, len=Length[id]; AllTrue[ Select[ Flatten[Table[FromDigits[Insert[id, n, i]], {i, len+1}, {n, 0, 9}], 1], #!=x&], CompositeQ]]; Select[ Prime[Range[3050000]], nipQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 12 2018 *)
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PROG
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(Python)
from sympy import isprime
from itertools import islice
def ok(n):
if not isprime(n): return False
s = str(n)
for c in "0123456789":
for k in range(len(s)+1):
w = s + c if k == 0 else s[:-k] + c + s[-k:]
if w[0] != "0" and isprime(int(w)): return False
return True
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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