Strobogrammatic prime
Encyclopedia
A strobogrammatic prime is a prime number
that, given a base and given a set of glyph
s, appears the same whether viewed normally or upside down. In base 10, given a set of glyphs where 0, 1 and 8 are symmetrical around the horizontal axis, and 6 and 9 are the same as each other upside down, (such as the digit characters in ASCII
using the font Stylus BT, or on the seven-segment display
of a calculator), the first few strobogrammatic primes are:
Although amateur aficionados of mathematics are quite interested in this concept, professional mathematicians generally are not. Like the concept of repunit primes and palindromic prime
s, the concept of strobogrammatic primes is base-dependent
. But the concept of strobogrammatic primes is not neatly expressible algebraically, the way that the concept of repunit primes is, or even the concept of palindromic primes.
There are sets of glyphs for writing numbers in base 10, such as the Devanagari
and Gurmukhi of India
in which the primes listed above are not strobogrammatic at all.
In binary, given a glyph for 1 consisting of a single line without hooks or serifs, all Mersenne prime
s are strobogrammatic. Palindromic primes in binary are also strobogrammatic.
Dihedral prime
s that don't use 2 or 5 are also strobogrammatic primes.
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
that, given a base and given a set of glyph
Glyph
A glyph is an element of writing: an individual mark on a written medium that contributes to the meaning of what is written. A glyph is made up of one or more graphemes....
s, appears the same whether viewed normally or upside down. In base 10, given a set of glyphs where 0, 1 and 8 are symmetrical around the horizontal axis, and 6 and 9 are the same as each other upside down, (such as the digit characters in ASCII
ASCII
The American Standard Code for Information Interchange is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text...
using the font Stylus BT, or on the seven-segment display
Seven-segment display
A seven-segment display , or seven-segment indicator, is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot-matrix displays...
of a calculator), the first few strobogrammatic primes are:
- 1111 (number)11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name...
, 101101 (number)101 is the natural number following 100 and preceding 102.It is variously pronounced "one hundred and one" / "a hundred and one", "one hundred one" / "a hundred one", and "one oh one"...
, 181181 (number)181 is the natural number between 180 and 182.-In mathematics:* 181 is an odd number* 181 is a centered number** 181 is a centered pentagonal number** 181 is a centered 12-gonal number** 181 is a centered 18-gonal number...
, 619, 16091, 18181
Although amateur aficionados of mathematics are quite interested in this concept, professional mathematicians generally are not. Like the concept of repunit primes and palindromic prime
Palindromic prime
A palindromic prime is a prime number that is also a palindromic number. Palindromicity depends on the base of the numbering system and its writing conventions, while primality is independent of such concerns...
s, the concept of strobogrammatic primes is base-dependent
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
. But the concept of strobogrammatic primes is not neatly expressible algebraically, the way that the concept of repunit primes is, or even the concept of palindromic primes.
There are sets of glyphs for writing numbers in base 10, such as the Devanagari
Devanagari
Devanagari |deva]]" and "nāgarī" ), also called Nagari , is an abugida alphabet of India and Nepal...
and Gurmukhi of India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
in which the primes listed above are not strobogrammatic at all.
In binary, given a glyph for 1 consisting of a single line without hooks or serifs, all Mersenne prime
Mersenne prime
In mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
s are strobogrammatic. Palindromic primes in binary are also strobogrammatic.
Dihedral prime
Dihedral prime
A dihedral prime or dihedral calculator prime is a prime number that still reads like itself or another prime number when read in a seven-segment display, regardless of orientation , and surface...
s that don't use 2 or 5 are also strobogrammatic primes.