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The given sequence is : $31,331,3331,33331....$ where the $n^{th}$ number has n $3$'s followed by a $1$. The question asked is to find are all the numbers prime? If not all how many terms from start are prime (e.g. first 30 terms , etc.) I'm completely blank of how do we approach such questions. Any reference or ideas ?

brainst
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    Turns out $333333331=1719607843$. All the previous terms are prime. Immediately, $3333333331=6734952947$, and $33333333331=307*108577633$. There seems to be absolutely no pattern whatsoever. Well, the next two terms are also not prime! – Sarvesh Ravichandran Iyer Apr 21 '16 at 05:02
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    http://math.stackexchange.com/questions/542634/31-331-3331-33331-333331-3333331-33333331-are-prime – Alex Apr 21 '16 at 05:03
  • But how do you tell this without any prior knowledge about the same? – brainst Apr 21 '16 at 05:03
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    You don't. ${}{}{}$ – Mariano Suárez-Álvarez Apr 21 '16 at 05:03
  • @MarianoSuárez-Alvarez Well this question was asked in my high school(12th grade) examination :/ – brainst Apr 21 '16 at 05:04
  • This is not a duplicate of that question. Neither the question nor the answers there ask or tell how to find out how many terms from the start are prime. They only deal with the much easier task of deciding whether there are any composite numbers in the sequence at all. Thus I believe the question should be reopened. – joriki Apr 21 '16 at 06:27
  • Somewhat related to Goldbach's theorem? – N.S.JOHN Apr 21 '16 at 07:52

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