Räuberzahl

Räuberzahl is a term used in number theory to describe a specific type of prime number. A prime number is called a Räuberzahl if it remains prime when its last digit is repeatedly removed. For example, the prime number 3797 is a Räuberzahl because 3797 is prime, 379 is prime, 37 is prime, and 3 is prime.

The concept is related to left-truncatable primes, where digits are removed from the left. Räuberzahlen are also known as right-truncatable primes. The first few Räuberzahlen are 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797, 5939, 7193, 7331, 7333, 7393.

The number of digits in a Räuberzahl is limited. If a Räuberzahl has more than four digits, it must contain the digit 3 or 7. Furthermore, if a Räuberzahl has more than three digits, it cannot contain the digits 0, 1, 4, 6, 8, or 9. The largest known Räuberzahl has 21 digits. The study of Räuberzahlen is a niche area within number theory, often explored by amateur mathematicians and puzzle enthusiasts.