A Wilson prime, named after English mathematician John Wilson, is a prime number p such that p2 divides (p − 1)! + 1, where "!" denotes the factorial function; compare this with Wilson's theorem, which states that every prime p divides (p − 1)! + 1.
The only known Wilson primes are 5, 13, and 563 (sequence A007540 in OEIS); if any others exist, they must be greater than 2×1013. It has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson primes in an interval is about log(log(y)/log(x)).
Several computer searches have been done in the hope of finding new Wilson primes. The Ibercivis distributed computing project includes a search for Wilson primes. Another search is coordinated at the mersenneforum.
Read more about Wilson Prime: Near-Wilson Primes
Famous quotes containing the words wilson and/or prime:
“The kind of guts that can get us all killed.”
—Michael Wilson (1914–1978)
“No woman in my time will be Prime Minister or Chancellor or Foreign Secretary—not the top jobs. Anyway I wouldn’t want to be Prime Minister. You have to give yourself 100%.”
—Margaret Thatcher (b. 1925)