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truncatable prime

A prime number n that remains a prime when digits are deleted from it one at a time. For example 410256793 is a truncatable prime because each number created by the removal of the digit underlined produces a new prime: 410256793, 41256793, 4125673, 415673, 45673, 4567, 467, 67, 7. It is conjectured that there are infinitely many of these primes. If the digits from a prime can be deleted only from the right to leave a prime, then n is called a right truncatable prime. If they can be deleted only from the left to leave a prime, then n is a left truncatable prime. The list of primes from which any digit can be deleted at each step to leave a prime is very short indeed, because it demands that each digit be a prime and also that no digit occurs twice. Only these numbers satisfy this requirement: 2, 3, 5, 7, 23, 37, 53 and 73.

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