Truncatable prime number

The trunkierbaren primes (Engl. Primes truncatable of lat. Truncare, off or curtail, cut back (comparable), lop, cancel, maim) are a subset of the prime numbers , the (right- or left-sided) on continued cutting their rates by as stay ahead of prime. One differentiates depending on the direction of cutting

• right-truncatable (R-truncable),
• left-truncatable (L-truncable) or
• Both sides can be truncated (bit truncated), ie both right and left truncated prime numbers.

Which prime numbers can be truncated depends on the number system used .

Right truncable prime numbers

Right-truncated prime numbers are prime numbers where omitting any number of the last digits leads to a prime number again.

In the decimal system, for example, the number 317 fulfills this property: 317, 31 and 3 are prime numbers. Thus 31 is also a right truncable prime number.

In the decimal system there are exactly 83 right truncable prime numbers. The first in this system are the numbers 2, 3, 5, 7, 23, 29, the largest in the decimal system is the number 73,939,133.

Right-drunk primes are also occasionally referred to as “Snowball Primes”, “Super Primes” and “Prime Primes”.

27 of the 83 decimal right truncation prime numbers cannot be extended to a larger prime number by adding another digit, the remaining 56 result from them by truncating digits.

Left-trunkable prime numbers

Left trunkable prime numbers are prime numbers,

• in which there is no digit zero anywhere,
• where the omission of any number of leading digits leads to a prime number again.

For example, in the decimal system, the number 632,647 has these properties because 632,647, 32,647, 2,647, 647, 47, and 7 are prime numbers. In the decimal system there are exactly 4260 prime numbers that can be left truncated . The largest of them is the number 357,686,312,646,216,567,629,137.

Prime numbers that can be truncated on both sides

In the decimal system, 2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3,137, 3,797 and 739,397 are the only prime numbers that can be truncated both left and right.

literature

• David Graham Wells: Prime Numbers. The Most Mysterious Figures in Math . Wiley, Hoboken NJ 2005, ISBN 0-471-46234-9 .
• IO Angell, HJ Godwin: On Truncatable Primes . In: Mathematics of Computation . tape 31 , 1977, ISSN  0025-5718 , pp. 265-267 .

Web links

• Eric W. Weisstein : Truncatable Prime . In: MathWorld (English).
• Chris Caldwell: Left-truncatable Prime and Right-truncatable Prime in The Prime Glossary .
• Patrick De Geest: List of the 4260 left-truncatable primes (without the zero digit) at World! Of Numbers (English).