Michael Goetz Volunteer moderator Project administrator Project scientist Send message Joined: 21 Jan 10 Posts: 13045 ID: 53948 Credit: 202,848,764 RAC: 96,051
What does "Factors found" mean? Thank you.
The process of searching for prime numbers starts with a large set of candidates. The status of each individual candidate (number) is initially unknown. It's either prime, or more likely, it's composite, but we don't know which.
Testing each individual number takes a long time, so we use a more efficient strategy: We first run a sieve, which rapidly is able to establish that many of the candidates are composite. Once we know a candidate is composite, we're done with it and don't need to consider it anymore.
Once we're done with the sieve, we're left with a much smaller set of candidates whose status is unknown. We then test this smaller set, one candidate at a time, with a program such as LLR or Genefer to determine its final status as prime or composite. (Genefer actually tests for a candidate being a "probable prime", but that's not relevant to this discussion.)
Now, back to your question. When the sieve proves that a candidate is composite, it does so by finding a factor of that candidate, i.e., it finds a small prime number that divides the candidate. The statistics showing number of factors found is therefore indicating how many candidates your sieve tasks have proven to be composite.
(And, in case your next question is "How can I see my factors?", you can't. We don't store that information. The number of factors found at the beginning of a sieve is prohibitively huge, and storing a record of who found what is impractical.)
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