Problem 60760. Find the closest canyon prime

Created by ChrisR

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My wife and I celebrated our honeymoon and most recent anniversary in Yellowstone and Grand Teton National Parks. After returning from our latest trip, I made her a word puzzle involving geysers, mud pots, and canyons. Because canyons form when rock erodes and walls remain, a canyon in the puzzle was a word that could erode two or more letters from the interior to form a new word, leaving at least one of the original letters on each side. For example, if TOPLAS is eroded from PROTOPLASM, then PROM is formed.
This problem deals with canyon primes, defined as a prime number that can erode two or more consecutive interior digits, leaving at least one original digit on each side, and become a new prime. 4813 and 4817 are both canyon primes because eroding 81 from both leaves 43 and 47, which are prime. 29411 is a canyon prime because eroding 94 leaves 211, which is prime. 299623 is a canyon prime because eroding 996 leaves 223, which is prime.
Write a function that produces the canyon prime closest to the input number. If two numbers are equally distant from the input, choose the smaller.

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Last Solution submitted on Nov 23, 2024

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William on 12 Nov 2024 at 14:34

Chris - This is a clever problem! Is it a condition that the eroded inner digits of a canyon prime be *consecutive*? In Test #6, my solution is identifying 99833 as a closer canyon prime than 99828, on the basis that 99833 is prime and 983 is prime. In that case, there are two canyons!

ChrisR on 22 Nov 2024 at 14:30

Good question. I clarified my completely arbitrary definition of canyon primes to include that the digits must be consecutive. But if you know of good hikes to river cross-sections with multiple canyons, please tell me!

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Problem 60760. Find the closest canyon prime

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Problem 60760. Find the closest canyon prime

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