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PrimePi limitations

• To: mathgroup at smc.vnet.net
• Subject: [mg54812] PrimePi limitations
• From: PbtoAu at aol.com
• Date: Wed, 2 Mar 2005 22:29:03 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

 
Hi Mathematica Mavens,
 
What is the size limit for PrimePi?  The docs show about 2^60.   On my 
machine it is 2.5e14.  Where does this limitation arise and how can  it be extended? 
 It seems unnecessarily low given the few minutes it takes  to return an 
answer for its maximum input.
 
For what size input does NextPrime break?  Either with an error or  suddenly 
very poor performance.  I saw where someone said Mathematica would  attempt 
NextPrime[10^100000].  Would it be fair to say that NextPrime does  not 
guarantee a prime, but that it does guarantee not to miss one?
 
Thanks for any information.
 
Best regards,
 
David Baugh