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Old 2019-02-13, 14:43   #1
davar55
 
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May 2004
New York City

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Default Primes from digit sequences

Consider the four numbers

111112222333445,
122333444455555,
544333222211111, and
555554444333221.

These are constructed out of the first n=five digits, in increasing or decreasing order,
each digit k repeated either k or 6-k times, to form these four decimal patterns.

The same four patterns can be formed for any positive integral number n, where
for k >= 10 all the digits in k are included k or n+1-k times at the appropriate space.

Find the first 3 values of n for which all four numbers are simultaneously prime.
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