Re: Two factors of (10^71-1)/9 = R71
- To: mathgroup at smc.vnet.net
- Subject: [mg30132] Re: [mg30125] Two factors of (10^71-1)/9 = R71
- From: BobHanlon at aol.com
- Date: Tue, 31 Jul 2001 04:27:07 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 2001/7/29 9:42:17 PM, seidovzf at yahoo.com writes: >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? > R71 = 241573142393627673576957439049* 45994811347886846310221728895223034301839; R71 == (10^71 - 1)/9 True The documentation for NumberTheory`FactorIntegerECM` states that it extends Mathematica's integer factoring to all numbers of 40 digits or less. R71 has 71 digits. It also states that the algorithm returns a single factor (not necessarily a prime). Mathematica recognizes R71 as non-Prime PrimeQ[R71]//Timing {0.03333333333284827*Second, False} Bob Hanlon Chantilly, VA USA