A number can be represented as a string of bits, and so can a program. A prime number that represents an executable program (on some reasonable operating system) is an executable prime!
The most common processor with one byte instructions is the x86 line and on these the least positive executable number is 195. The is the value of the one-byte program
According to Phil Carmody (see his well written link below), the three smallest executable primes on current hardwre are the two byte programs:
(These should execute fine on any x86 system.)
If we do not require that the prime run on a current system, then Phil suggests the least executable prime
is 199 (
What about a non-trivial prime? The first one ever found was a program that is apparantly functionally equivalent to Charles Hannum's tiny C version of deCSS. Phil Carmody altered the code slightly to make the compiled version shorter, and created an 1811-digit prime. See the first Prime Curios! link below.
See Also: Illegal
Related pages (outside of this work)