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Omni-MATH / Does there exist a prime number whose decimal representation is of the form…

Problem

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problem

Does there exist a prime number whose decimal representation is of the form 3811⋯113811\cdots11 (that is, consisting of the digits 33 and 88 in that order, followed by one or more digits 11)?
Plain-text mathematical notation (without MathML)
Does there exist a prime number whose decimal representation is of the form 3811⋯11 (that is, consisting of the digits 3 and 8 in that order, followed by one or more digits 1)?
Original LaTeX notation
Does there exist a prime number whose decimal representation is of the form $3811\cdots11$ (that is, consisting of the digits $3$ and $8$ in that order, followed by one or more digits $1$)?

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Source and history

Official source

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