Roger Hui wrote: > I believe you understate the overwhelming advantages > you have over Eratosthenes.
I just looked up the paper which popularized the Sieve: Samuel Horsley, The Sieve of Eratosthenes. Being an Account of His Method of Finding All the Prime Numbers. Philosophical Transactions 62 (1772) 327-347. (It's on JSTOR, if you have access.) What is interesting is that Eratosthenes sieve applied only to odd numbers, unlike the way we present it today: even numbers except for 2 were excluded a priori, and Eratosthenes' table contained only odd numbers. There is not much indication as to how he came up with it. On the notion of finding all divisors, Horsley notes This method requires indeed that the least prime divisor should be previously found; and, if the least prime divisor should happen to be a large number, as it is not assignable by any general method, the investigation of it by repreated tentations may be very tedious. John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
