Problem #37 Difficulty: 5%

Truncatable Primes

Solution Language: Python
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Problem Statement

The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.

Approach

The solution involves:

  1. Generating prime numbers systematically
  2. For each prime (excluding single-digit primes), checking all left truncations
  3. Checking all right truncations
  4. Verifying that all truncations are prime
  5. Summing the eleven primes that satisfy both conditions