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EMIRP pair inside a PRIME (Posted on 2023-10-19) Difficulty: 3 of 5
Find some primes that safely contain a pair of emirps. The emirps must be isolated from each other and from the outside world by a digit. It is as if the emirps are matter and anti-matter: they cannot touch or there will be a risk of catastrophic anihilation. And since we cannot tell which one is anti-matter, both must be isolated from each other and also the rest of the world. This is all in accordance with the ancient lore.

(1) What is the smallest 9-digit prime of the form: axyzbzyxc, where xyz and zyx are each 3-digit primes with distinct digits; and each letter a,b,c,x,y,z designates a different digit.
(2) Also find the largest.
(3) Now, same question for an 11-digit prime of the form awxyzbzyxwc; again different letters are distinct digits, where wxyz and zyxw are a pair of 4-digit emirps.
(4) Also find the largest.

Note: Emirps are primes whose reversal is a different prime.

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  Subject Author Date
Solutioncomputer solutionCharlie2023-10-19 10:02:26
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