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I want to know more about primality test , this is one of my question to determine if an integer odd number could be prime with below property in the question.

Question: Could be an odd integer number with repeat digits a prime ?

Note: for example a number as this :$474747\cdots$

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    Do you consider something like $31313$? If not, then repeating the number $n$ gives a number divisible by $n$, so unless $n=1$ it is composite. Look up repunits. – 2017-02-10
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    If $n= \overline{abcd\dots}$ meaning that the number $abcd\dots$ repeats then $n$ is divisible by $abcd\dots$. E.g. $474747=10101\times47$ – 2017-02-10
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    @ yes , i meant example :31313 , and i have a problem to formulate what i meant, for example :37377 i repeat the two digits and i keep one – 2017-02-10
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    $1111111111111111111$ is a prime number. – 2017-02-10
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    nice example you have – 2017-02-10
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    So you're talking about repeating a *group* of digits, not just one digit, right? – 2017-02-10
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    Take a look also at http://oeis.org/A173772 – 2017-02-10
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    We cannot say much about when a general number with such a pattern is prime. It was already pointed out that a full nontrivial period cannot lead to a prime. I do not think that we can do much more. – 2017-02-11

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$$1717171717171717171717171717171$$ is an example with $31$ digits

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    Is that a repunits number ? if yes that is contradict that Repunit number can't be a prime , then i want if there is any known proof about that , and thanks for your nice example – 2017-02-14
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    and I upvote for this example – 2017-02-14
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    @zeraouliarafik No, a repunit number is a number consisting of only one digit, for example $777777$. The repunits containing only ones have been checked for primality, some primes were found, but noone knows whether infinite or finite many such primes exist. – 2017-02-16
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Have you heard about repunits?