Mersenne: Re: The first 1000+ digit prime

2002-08-20 Thread EWMAYER
Tony Forbes writes: >We all know that A. Hurwitz discovered the Mersenne primes 2^4253 - 1 >and 2^4423 - 1 in 1961. > >(i) Were these the first two 1000+ digit primes discovered? As far as I know, yes (note that M3217, discovered in 1957 by Hans Riesel, was very close to 1000 decimal digits in l

RE: Mersenne: Reference Machine

2002-08-20 Thread Aaron Blosser
I'll have to go along with other comments, that using some ancient CPU seems odd, but then again, any baseline you use will end up being arbitrary anyway, so... whatever works. As for "prime95", I think that was more a reference to Windows 95, and there was the service version, priment (or ntprim

Mersenne: Reference Machine

2002-08-20 Thread Frank_A_L_I_N_Y
Anyone consider using a Cray as our benchmark? Also Anyone considering renaming prime95 considering it is 2002? Thanks Frank. _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ --

Re: Mersenne: Benchmarks / Reference Machine / Calculations

2002-08-20 Thread Dave Zook
Michael Vang highlights the fact that there are two different things that we can measure: 1) work accomplished, e.g. Mnumbers evaluated, iterations run, etc. 2) work effort expended, which requires evaluation of processor/system power.   The P4 versions (more efficient) accomplish more with

Mersenne: Re: ECM testing on Fermat numbers

2002-08-20 Thread Phil Moore
I have been running ECM curves on Fermat numbers lately on numbers of the form 2^(2^n) - 1 (rather than + 1, as in the definition of Fermat numbers.) The number 2^(2^n) - 1 is the product of all the Fermat number F0 through F(n-1), so by running a curve on M32768 = M(2^15), I can search for f

Re: Mersenne: Benchmarks / Reference Machine / Calculations

2002-08-20 Thread Michael Vang
> Really we need only consider IEEE single (24+8) & double (53+11) precision > types... the x87 80-bit format is not much different to double precision the > way we use it, and I'm not aware of any common hardware implementations of > other floating-point formats. At the risk of sounding dumb (Al

Re: Mersenne: Benchmarks / Reference Machine / Calculations

2002-08-20 Thread Brian J. Beesley
On Tuesday 20 August 2002 08:57, Paul Leyland wrote: > Anyone else here old enough to remember Meaningless Indicators of Processor > Speeds? Oh yes. My first boss used to rate CPUs in "Atlas power" > > All gigaflops are not created equal, unfortunately. Wordlength alone can > make a big diff

Re: Mersenne: The first 1000+ digit prime

2002-08-20 Thread Brian J. Beesley
On Tuesday 20 August 2002 16:32, Tony Forbes wrote: > We all know that A. Hurwitz discovered the Mersenne primes 2^4253 - 1 > and 2^4423 - 1 in 1961. > > (i) Were these the first two 1000+ digit primes discovered? Yes. See http://www.utm.edu/research/primes/notes/by_year.html#table2 > > (ii) If t

Mersenne: The first 1000+ digit prime

2002-08-20 Thread Tony Forbes
We all know that A. Hurwitz discovered the Mersenne primes 2^4253 - 1 and 2^4423 - 1 in 1961. (i) Were these the first two 1000+ digit primes discovered? (ii) If that is true, then is it generally accepted that the larger one (4423) was discovered first? (The story I heard was that left the

RE: Mersenne: Benchmarks / Reference Machine / Calculations

2002-08-20 Thread Paul Leyland
> Why even bother with that? Just use gigaflops or something that is not > hardware dependent at all... Ah, but which gigaflops? Anyone else here old enough to remember Meaningless Indicators of Processor Speeds? All gigaflops are not created equal, unfortunately. Wordlength alone can make a b