Truncatable prime
Type of number
In number theory, a left-truncatable prime is a prime number which, in a given base, contains no 0, and if the leading ("left") digit is successively removed, then all resulting numbers are prime. For example, 9137, since 9137, 137, 37 and 7 are all prime. Decimal representation is often assumed and always used in this article.
A right-truncatable prime is a prime which remains prime when the last ("right") digit is successively removed. 7393 is an example of a right-truncatable prime, since 7393, 739, 73, and 7 are all prime.
A left-and-right-truncatable prime is a prime which remains prime if the leading ("left") and last ("right") digits are simultaneously successively removed down to a one- or two-digit prime. 1825711 is an example of a left-and-right-truncatable prime, since 1825711, 82571, 257, and 5 are all prime.
In base 10, there are exactly 4260 left-truncatable primes, 83 right-truncatable primes, and 920,720,315 left-and-right-truncatable primes.
History
Author Leslie E. Card in early volumes of the Journal of Recreational Mathematics (which started its run in 1968) considered a topic close to that of right-truncatable primes, calling sequences that by adding digits to the right in sequence to an initial number not necessarily prime snowball primes.
Discussion of the topic dates to at least November 1969 issue of Mathematics Magazine, where truncatable primes were called prime primes by two co-authors (Murray Berg and John E. Walstrom).
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This entry incorporates text from “Truncatable prime” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.