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A069677
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Primes with either no internal digits or all internal digits are 2.
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9
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 127, 223, 227, 229, 421, 521, 523, 727, 821, 823, 827, 829, 929, 1223, 1229, 2221, 3221, 3229, 4229, 5227, 6221, 6229, 7229, 8221, 9221, 9227, 12227, 22229, 42221
(list;
graph;
refs;
listen;
history;
text;
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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Join[Prime[Range[25]], Select[Prime[Range[26, 4500]], Union[Most[ Rest[ IntegerDigits[ #]]]] =={2}&]] (* Harvey P. Dale, Aug 12 2021 *)
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PROG
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(PARI) uptoqdigits(n) = { my(ld = [1, 3, 7, 9]); n = max(n, 2); res = List(primes(primepi(97))); for(i = 1, n-2, twos = 20*(10^i\9); for(j = 1, 9, for(k = 1, #ld, c = j*10^(i+1) + twos + ld[k]; if(isprime(c), listput(res, c) ) ) ) ); Set(res) } \\ David A. Corneth, Aug 12 2021
(Python)
from sympy import isprime
def agen(maxdigits):
yield from [2, 3, 5, 7]
for d in range(2, maxdigits+1):
pow10, mid = 10**(d-1), 0 if d < 3 else 10*int('2'*(d-2))
cands = (a*pow10+mid+b for a in range(1, 10) for b in [1, 3, 7, 9])
yield from filter(isprime, cands)
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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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