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11, 101, 181, 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 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.