20050828, 22:18  #1 
"Kyle"
Feb 2005
Somewhere near M50..sshh!
1101111110_{2} Posts 
Shortcuts on large computations
Alright, quick question everyone. Is there a way to find the last few digits and the first few digits of a large number in exponent form, i.e. 2^2345343? I know that finding the last few digits would be easier, but finding more than the last 3 (as far as my mathematical knowledge goes, would take a very long time). And as for finding the first, say, 10 digits of the number...I have no idea how to do that. Is there an easy, fast way to find the first and last 10 digits of such a number, with any base?
Thanks. 
20050828, 22:26  #2  
Nov 2003
2^{2}·5·373 Posts 
Quote:
number theory. Just compute your number mod 10^k for your chosen k. Finding the first few digits is also easy and requires nothing more than second year high school algebra. Hint: "think logarithms". Of course, one needed to compute the log to sufficient accuracy, but that is easy. [but it does require some knowledge of infinite series or equivalent] 

20050829, 20:19  #3 
∂^{2}ω=0
Sep 2002
República de California
2·13·443 Posts 
For the leastsignificant D decimal digits, compute your desired number using modular binary exponentiation, with modulus 10^D.

20050903, 18:56  #4 
"Kyle"
Feb 2005
Somewhere near M50..sshh!
1101111110_{2} Posts 
Thanks :)

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
What should the "q" value increase to for GNFS/SNFS computations?  2147483647  Factoring  2  20161210 08:42 
Large FFT tweaking  Zerowalker  Information & Answers  8  20130419 15:01 
a^n mod m (with large n)  Romulas  Math  3  20100508 20:11 
NFS with 5 and 6 large primes  jasonp  Factoring  4  20071204 18:32 
very large exponents  pacionet  Data  4  20051104 20:10 