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Proof that there are infinitely many prime numbers starting with a given digit string

Let n be the representation of a natural number in a non-unary base. Is it a prefix of the representation of a prime number over the same base?

For example: in decimal, the answer for 10 is yes, because 103 is prime. Is this true for every number?

EDIT: As Henning Makholm has pointed out, this question has been asked before: Proof that there are infinitely many prime numbers starting with a given digit string

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Yes. You need only to use basic results about the distributions of primes to guarantee that, for example, a prime number must exist between 100 and 109, or 1000-1099, etc. You should be able to easily generalize this.

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  • $\begingroup$ This simply restates the question and is insubstantial. $\endgroup$ Jun 12, 2015 at 11:00

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