20091031, 16:25  #1 
Oct 2009
3 Posts 
How many digits?
If I'm working on an LL test of N = 2^48,000,000  1, for example, is there any way for me to find how many digits N has?
Thanks! 
20091031, 16:55  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
(with p being the exponent, the p in 2^p1) The exact number is int(log_10(2^p)+1) = int(log_10(2)*p+1), which is roughly 0.3*p. Your example has exactly 14449440 (14.4 million) digits.
http://mersennearies.sili.net/digits.php calculates log_10(2^N), or the reverse (enter the digits to find the bits). int(n) means the integer part of n. (e.g. int(4.8)=int(4.2)=int(4)=4) log_10(2) is the base 10 logarithm of 2. (i.e. 10^(log_10(2))=2; it's about 0.3) Last fiddled with by MiniGeek on 20091031 at 17:03 
20091031, 17:20  #3  
Oct 2009
3 Posts 
Quote:


20091031, 17:37  #4 
Nov 2003
2×3×11×113 Posts 

20091031, 18:34  #5 
Aug 2006
2·3·977 Posts 

20091031, 19:39  #6 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
True, but being able to connect the dots to realize that the exact formula for the number of digits in a number of the form 2^p1 is int(log_10(2)*p+1) is not exactly what you learn when learning basic logarithms. Basic logarithmic theory would suggest that it's about log_10(2^p)=log_10(2)*p, but to recognize the problem as related to logarithms and rederive the exact formula would be a bit more difficult than you all seem to imply. And this is all assuming the OP has even learned logarithms.

20091101, 00:42  #7  
Aug 2006
2·3·977 Posts 
Quote:


20091101, 04:20  #8 
Oct 2009
3 Posts 

20091101, 20:05  #9 
Oct 2008
n00bville
5^{2}·29 Posts 
There is somewhere in the forum a Windows program which calculates the exact value ... search for it

20091101, 20:55  #10 
Aug 2006
2×3×977 Posts 

20091101, 21:57  #11  
Nov 2003
2×3×11×113 Posts 
Quote:
IN CLASS in the 8th grade. i.e. the last year BEFORE high school. Solving 2^x = 10^z is fundamental! It is totally trivial. Last fiddled with by R.D. Silverman on 20091101 at 21:57 Reason: typo 

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