
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 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 onebyte 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 nontrivial 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 1811digit prime. See the first Prime Curios! link below.
See Also: Illegal Related pages (outside of this work)
Chris K. Caldwell © 19992019 (all rights reserved)
