Two factors of (10^71-1)/9 = R71

*To*: mathgroup at smc.vnet.net*Subject*: [mg30125] Two factors of (10^71-1)/9 = R71*From*: seidovzf at yahoo.com (Zakir F. Seidov)*Date*: Sun, 29 Jul 2001 21:26:17 -0400 (EDT)*Organization*: The Math Forum*References*: <6kajko$2bn@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

The number William Mopppett wrote: ================ (10^71 - 1)/9 is R71, repunit, number with "all ones". And it has two factors: R71 = 241573142393627673576957439049 *45994811347886846310221728895223034301839 See, e.g., http://www.ping.be/~ping6758/repunits.htm But suprisingly enough, when, before looking for "repunit"s in 37.com, I asked my PC to work for saturday, its Mathematica session was: $Version 4.0 for Microsoft Windows (December 5, 1999) << NumberTheory`FactorIntegerECM` Timing[f = FactorIntegerECM[(2^128 + 1)/f] ] {793.95 Second, 59649589127497217} (* good, but...*) Timing[FactorIntegerECM[(10^71 - 1)/9 ]] {112642. Second, \ 111111111111111111111111111111111111111111111111111111111111111\ 11111111} (* ??!! *) That is Mathematica (or my PC?) considers R71 as prime! And this is a real suprise and hence the question to Mathematica experts: how it can be? Zakir F. Seidov seidovzf at yahoo.com %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%% Subject: [mg30125] RE: factor Author: Ersek_Ted%PAX1A at mr.nawcad.navy.mil Organization: Steven M. Christensen and Associates, Inc and MathTensor, Inc. William Mopppett wrote: | |Can anyone give me a factor of (10^71 - 1)/9 Mathematica 3.0 says it is |not prime email |wmoppet at nsw.bigpond.net.au | | The attempt below is probably the most effective way to do this. My 90 Mhz Pentium worked on it for 14 hours and still didn't find a factor. The documentation makes it clear you will may not get an answer in a short amount of time. It also says it is designed to find factors up to about 18 digits in 3 hours on a "workstation" (what ever that is). Well it seems all the prime factors of this number have 18 to 35 digits, and it has two, three, or four prime factors. The number of potential prime factors to consider is roughly, ( 10^35/Log[10^35] - 10^18/Log[10^18] ) = ( 1.2 * 10^33 ) !! In[1]:= <<NumberTheory`FactorIntegerECM` In[2]:= FactorIntegerECM[(10^71 - 1)/9 ] (* still waiting *) ___________________________________ Perhaps you can do better by specifying a value for one or more of the options. In[3]:= Options[FactorIntegerECM] Out[3]= {FactorSize -> Automatic, CurveNumber -> Automatic, CurveCountLimit -> 10000} __________________________________ Ted Ersek