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A366826
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Composite numbers whose proper substrings (of their decimal expansions) are all primes.
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0
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4, 6, 8, 9, 22, 25, 27, 32, 33, 35, 52, 55, 57, 72, 75, 77, 237, 537, 737
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OFFSET
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1,1
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COMMENTS
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There are no terms greater than 999 because the only three-digit prime whose substrings are all primes is 373 (see A085823) and prepending or appending any prime digit to it would create a different three-digit substring.
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LINKS
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EXAMPLE
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237 is included because it is composite and 2, 3, 7, 23 and 37 are all primes.
4 is included because it is composite and has no proper substrings.
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PROG
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(Python)
from itertools import combinations
from sympy import isprime
for n in range(2, 1000):
if not isprime(n):
properSubstrings = set(
int(str(n)[start:end]) for (start, end)
in combinations(range(len(str(n)) + 1), 2)
) - set((n, ))
if all(isprime(s) for s in properSubstrings):
print(n, end=', ')
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CROSSREFS
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KEYWORD
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base,fini,full,nonn
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AUTHOR
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STATUS
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approved
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