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MathGroup Archive 2007

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PowerMod[] - Mathematica 5.0 - problem/error/bug?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73029] PowerMod[] - Mathematica 5.0 - problem/error/bug?
  • From: Anton Vrba <antonvrba at yahoo.com>
  • Date: Tue, 30 Jan 2007 06:36:13 -0500 (EST)

In Mathematica 5.0 I found on my system the following incorrect result regarding the PowerMod[] function
   
  You agree that PowerMod[2,17 p, p]=2^17 for p prime and p>2^17 
   
  Mathematica 5.0 calculates PowerMod[2,17 p, p] as 2^2 
  for p=126322571 through to p=2147483647. (one can change the 2 to any base and the wrong answer base^2 is calculated)
   
  below the notebook file converted to text format.
   
  Have I a problem in my system? or is this a Mathematica 5.0 bug or possibly a new Pentium bug? 
   
  best regards
  Anton
   
  In[60]:=
  p=Prime[123456780]
  y=PowerMod[2,17  p,p]
  FactorInteger[y]
  "y is the correct result"
   
  p=Prime[103456780]
  y=PowerMod[2,17  p,p]
  FactorInteger[y]
  "y should equal 2^17 and not 2^2" 
   
  m=5
  y=PowerMod[2,(2^(32 m)-1)  p,p]
  FactorInteger[y]
  m=12
  y=PowerMod[2,(2^(32 m)-1)  p,p]
  FactorInteger[y]
  "y equal 2^(m+1) is a cute result"
   
  Out[60]=2543568329
  Out[61]=131072
  Out[62]={{2,17}}
  Out[63]=y is the correct result
  Out[64]=2112226087
  Out[65]=4
  Out[66]={{2,2}}
  Out[67]=y should equal 2^17 and not 2^2
  Out[68]=5
  Out[69]=64
  Out[70]={{2,6}}
  Out[71]=12
  Out[72]=8192
  Out[73]={{2,13}}
  Out[74]=y equal 2^(m+1) is a cute result
   
  In[75]:=
  "here is the range of the error"
  p=Prime[7181138]
  FactorInteger[PowerMod[2,17  p,p]]
  p=Prime[7181138+1]
  FactorInteger[PowerMod[2,17  p,p]]
  p=Prime[105097565]
  FactorInteger[PowerMod[2,17  p,p]]
  p=Prime[105097565+1]
  FactorInteger[PowerMod[2,17  p,p]]
  Out[75]=here is the range of the error
  Out[76]=126322543
  Out[77]={{2,17}}
  Out[78]=126322571
  Out[79]={{2,2}}
  Out[80]=2147483647
  Out[81]={{2,2}}
  Out[82]=2147483659
  Out[83]={{2,17}}
   



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