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A068689
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Primes which are a sandwich of numbers made of only one decimal digit between two 9's.
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3
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OFFSET
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1,1
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COMMENTS
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Conjecture: Inner digits 1, 2 and 8 are the only repeating digits for which the resulting numbers can be prime for outer digits 9. I.e., 9444..4449, 9555..5559, 9777..7779 are composite. The cases for inner digits 0, 3, 6 and 9 give composite numbers. - Cino Hilliard, Jul 11 2005
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LINKS
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PROG
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(PARI) lista(nn) = my(list = List(), p); for (n=1, nn, for (k=1, 8, my(d=vector(n, i, k)); d = concat(9, d); d = concat(d, 9); if (ispseudoprime(p=fromdigits(d)), listput(list, p)); ); ); Vec(list); \\ Michel Marcus, Jan 28 2023
(Python)
from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for m in "124578" if isprime(t:=int("9" + m*i + "9")))
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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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EXTENSIONS
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STATUS
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approved
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