Emirp primE

Problem #157

Tags: mathematics puzzle

Who solved this?

Thanks to MoffSerge for suggesting this problem!

Some primes are Emirp. This word is just "prime" reversed. Such primes if their decimal notation is reversed give another prime value.

The number 13 for example have such a property - if we write down its digits in reverse order the resulting value 31 also appears to be prime!

Among the two-digit primes here is even more interesting one: 37 if reversed becomes 73 and both of them are primes. Moreover they are 12th and 21st primes (if we agree that 2 is the 1st) and these two numbers also are each other's mirror image. Though of course such coincidence is rare one and hard to check for large values.

Your goal is simple. For given X you are to find closest next emirp prime (i.e. value greater or equal to X which is prime itself and its reverse in decimal notation is also a prime).

Input data will contain the amound of primes to find in the first line.
Next lines will contain a single X each.
Answer should contain closest emirp prime for each of X-s.


input data:

11 31 71

Values of X could be large enough so you may want to use some advanced primality test, perhaps non-deterministic one.

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