About These Composites

These factorizations are not, strictly speaking, necessary for the Odd Perfect Number Search. In most cases the factor chain in an odd perfect proof can be extended if at least one factor is known. When factoring numbers to fill the hints file, the remaining composites are sometimes in the range where Quadratic Sieve or personal SNFS is applicable. Having these factors will make some proofs shorter, and many people feel that proofs will full factorizations are more aesthetic, so although not strictly necessary, these factorizations are of some interest. It's fun to do small factoring and hard to find candidates that anyone cares about, so these less interesting candidates are provided as a service.

Non-Qualified Composites

In addition to the composites listed here, I also have composties from 105 to 159 digits that have had very little ECM work. Experience has shown that if posted here, many people will begin GNFS or SNFS immediately and eventually find small factors that could have been found quickly with ECM. To reduce such waste of factoring power, these numbers are only available through email.

I welcome both ECM-only users and ECM-before-NFS users. Numbers receiving adequate ECM-only work will then be posted to this composite page. Send requests, including desired size of composites, to QS at odd perfect dot org.

A few small batches of QS-appropriate 87-109 digit numbers are also available by email. These are not posted because I often get three complete factorizations before I can mark them reserved, a waste of computing power.

Personal Factoring Candidates

I originally proposed numbers under 105 digits as suitable for Quadratic Sieve, but it has been pointed out that many of these small candidates are also well suited for SNFS. I'm running out of small candidates, and some people have asked about large candidates. I don't know what size numbers will appeal to people for SNFS, so I've included some variety. I'll keep all small candidates here and will update the larger ones based on interest.

These composites have arisen in the process of seeking factors for the Odd Perfect Number Search. None of these factors are necessary to clear road blocks at this time.

Email me at QS at odd perfect dot org to reserve one.