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From: lambert@mcvax.uucp (Lambert Meertens)
Newsgroups: sci.math.symbolic
Subject: Re: Another factorization request.
Message-ID: <7148@boring.mcvax.UUCP>
Date: Sun, 16-Nov-86 11:22:06 EST
Article-I.D.: boring.7148
Posted: Sun Nov 16 11:22:06 1986
Date-Received: Sun, 16-Nov-86 21:13:06 EST
References: <2380002@hpsadla.HP>
Reply-To: lambert@boring.uucp (Lambert Meertens)
Organization: CWI, Amsterdam
Lines: 75
Summary: 2^200 with some pseudo-random digits
Apparently-To: rnews@mcvax


In article <2380002@hpsadla.HP> jimh@hpsadla.HP (Jim Horn) quotes from the
"Canadian Farm & Home Almanac" the following "Argument Clincher":

> The possibility of two persons having identical fingerprints is one chance in
>
>   1606937974174171729761809705564167968221676069604401795301376.

The number quoted is suspiciously close to 2^200 =

    1606938044258990275541962092341162602522202993782792835301376.

That would correspond to twenty yes/no fingerprint characteristics for each
finger.  The question remains where the middle segment of digits comes from.
One guess is that someone determined the leading digits using a six-place
log table, the final digits using modular arithmetic, and proceeded to fill
in the rest at random, thinking no-one would bother to check it out.
Another possibility is that the (human) computer really goofed in doing the
arithmetic.  I tried to reconstruct a scenario in which the number is
obtained by repeated doubling in decimal arithmetic while being subjected
to a few random errors in the digits.  The simplest I could find (but I did
not try that hard) is given below.  A "v" stands for an assumed error.  I
have no idea if the number of v's is significantly lower than needed to
explain an arbitrary random middle segment.

                 22300745198530623141535718272648361505980416 = 2^144
                                 vvvvvv   v                  
                 22300745198530624250645715272648361505980416
                 -------------------------------------------- * 2^3
                178405961588244994005165722181186892047843328
                                           vvv               
                178405961588244994005165722270186892047843328
                --------------------------------------------- * 2^4
               2854495385411919904082651556322990272765493248
                                             vvv             
               2854495385411919904082651556323700272765493248
               ---------------------------------------------- * 2^2
              11417981541647679616330606225294801091061972992
                                                v            
              11417981541647679616330606225294802091061972992
              ----------------------------------------------- * 2^1
              22835963083295359232661212450589604182123945984
                                                 v           
              22835963083295359232661212450589604282123945984
              ----------------------------------------------- * 2^2
              91343852333181436930644849802358417128495783936
                                                  v          
              91343852333181436930644849802358417158495783936
              ----------------------------------------------- * 2^1
             182687704666362873861289699604716834316991567872
                         vvv                                 
             182687704666256873861289699604716834316991567872
             ------------------------------------------------ * 2^2
             730750818665027495445158798418867337267966271488
                                                   v         
             730750818665027495445158798418867337268966271488
             ------------------------------------------------ * 2^1
            1461501637330054990890317596837734674537932542976
                                                   vvv       
            1461501637330054990890317596837734674538002542976
            ------------------------------------------------- * 2^4
           23384026197280879854245081549403754792608040687616
                                                     v       
           23384026197280879854245081549403754792608030687616
           -------------------------------------------------- * 2^13
       191561942608124967765975708052715559261044987392950272
                vv                                           
       191561942598124967765975708052715559261044987392950272
       ------------------------------------------------------ * 2^23
1606938044174171889601405952376674162141676069604401795301376
      vvv                                                    
1606937974174171889601405952376674162141676069604401795301376

-- 

Lambert Meertens, CWI, Amsterdam; lambert@mcvax.UUCP