From: Thane Plambeck <thane@best.com>

At the ams.org, and many other places (including GIMPS), the phrase "The Largest Known Prime" is used repeatedly. There must be some other way to report Mersenne prime progress without using this unfortunate phrase, which finds itself into the media and can be easily misconstrued as "Largest Prime Found."

I don't have a good replacement though. Maybe just "Larger" instead?

But the "Largest Known Prime" does mean the "Largest Prime Found". There is no misconstrual. To what do you want the phrase "Largest Known Prime" to refer, if not the largest prime found? And what to you mean by the "Mersenne prime progress" anyway? All the knowledge in the world about composite Mersennes (which is what most of the information, by count, coming out of GIMPS is) does not affect in any way the knowledge of what the largest prime found is. However, the idea that somehow Mersenne prime testing progress is tied to the worlds largest prime is conveniently forgetting Riesel and the Amdahl 6, and also ignoring the fact that there are other current projects which would have a more favourable chance of finding a prime larger than the current largest known one, if only they would have the popularity of GIMPS. For example, Yves Gallot's Generalised Fermat Number (GFN) hunt is looking at ranges of numbers all of which have a similar size (this helps keep the density roughly constant), has an exceptionally simple right-angle DWT transform for fast modular arithmetic (simpler than Mersenne's IBDWT, basically the same work-factor), can be sieved rather than simply trial-divided, and which have an exceptionally high prime density (Mersennes are sparse due to the primality criterion on the exponent). If it had the same CPU resources as GIMPS it's yield would be roughly twice GIMPS's (as measured by the sum of the cubes of the logs, extrapolating the current yield from their limited resources). My own PIES project looks at ranges of Generalised Eisenstein Fermat numbers (the Phi(3*2^n,b) equivalents to GFN's Phi(2^n,b), corresponding to norms of Eisenstein integers b^(2^n)+omega rather than GFN's norms of b^(2^n)+i in the complex plane) which have the same similar-size property as Yves' GFNs, has a dogleg-DWT (my own coinage, I've not seen anyone use such a transform before, but it has the same work-factor as an IBDWT and a right-angle-DWT), can also be sieved, and has _twice_ the density of Yves' GFNs, thus having a higher chance of finding results in the finite ranges (bounded by FFT rounding errors) available. (It is the 4-th highest yielding project despite only having a handful of testers with a handful of machines, many of which are obsolete technology.) The days of the Mersenne's dominance because of the 3x work-factor boost from its IBDWT is now over. It's now only dominant as it has unimaginably more boxes working on it. Phil ===== When inserting a CD, hold down shift to stop the AutoRun feature In the Device Manager, disable the SbcpHid device. http://www.cs.princeton.edu/~jhalderm/cd3/ __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com