Strobogrammatic prime
A strobogrammatic prime is a prime number that, given a base and given a set of glyphs, 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:
- 11, 101, 181, 619, 16091, 18181, 19861, 61819, 116911, 119611, 160091, 169691, 191161, 196961, 686989, 688889, ... (sequence A007597 in the OEIS)
Although amateur aficionados of mathematics are quite interested in this concept, professional mathematicians generally are not. Like the concept of repunit primes and palindromic primes, 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 primes are strobogrammatic. Palindromic primes in binary are also strobogrammatic.
Dihedral primes that do not use 2 or 5 are also strobogrammatic primes.
In duodecimal, they are: (using inverted two and three for ten and eleven, respectively)
- 11, 3Ɛ, 111, 181, 30Ɛ, 12ᘔ1, 13Ɛ1, 311Ɛ, 396Ɛ, 3ᘔ2Ɛ, 11111, 11811, 130Ɛ1, 16191, 18881, 1Ɛ831, 3000Ɛ, 3181Ɛ, 328ᘔƐ, 331ƐƐ, 338ƐƐ, 3689Ɛ, 3818Ɛ, 3888Ɛ, ...