The following warnings occurred:
Warning [2] Undefined array key 24184 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 24357 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 24843 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $thread - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $fid - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 24843 - Line: 331 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 331 errorHandler->error_callback
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 304 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $theme - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $theme - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $lang - Line: 5 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 5 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Attempt to read property "messages_in_thread" on null - Line: 5 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 5 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks





Factorials of Large Numbers



#4

I posted an HP-11C/41C program in the Software Library (it's now the first entry) and asked for feedback from anyone who has a real use for this...where n! >= 1E100

Any one got any news for me?



(And for those smart guys with HP-71 or newer calcs with number range up to 1E500, same applies to you but for >= 1E500 !)

Gordon.


#5

Hi...

Whoa, this brings back memories of a 'wasted' summer in high school (1980?) tinkering with my ol' TI58! (Didn't get my 41C til Christmas in my senior year - and then fooling w/system architecture/SP/ byte jumping etc took over...)

Wrote various "big factorial" programs, including log(n!) programs and approximations.

Stirling's Approx. works progressively better for larger and larger values of n, but has to be 'warped' for moderately useful performance for, say, n<69.

n! ~= sqrt(2*pi*n) * (n/e)^n
and
log(n!) ~= 0.5*log(2*pi*n) + n*log(n/e)

Anyway I still remember that 10,000!~= 2.645x10^35659
and 1,000!~= n.nnnx10^2567
100!~= 9.332x10^157...

Nifty little thing:
Number of trailing zeros of n!:
Trailing zero = multiple of 10. We have an excess of factors of two in a factorial (after all, every other number is even!) so every term in factorial that has a 5 or power thereof determines a trailing zero.

Thus:

int(n/5)+int(n/25)+int(n/125)+int(n/625)+int(n/5^5)...

gives us number of trailing zeros in n! . 1000! has, IIRC, 249 trailing zeros and 10,000! has 2499 trailing zeros.

Factorials are neat. Remember finding out about companion gamma function (I *knew* there must be something continuous over n>=0 for something factorial-like.)

That was a fun summer...

Bill Wiese
San Jose, CA


#6

Hi Bill, I'm glad you enjoyed my message.

Did you try the program?

I was beginning to think that no one was interested!



Perhaps I should ask for the prog to be posted in the HP-41 software section and more people would look at it.

Best Wishes.


Possibly Related Threads…
Thread Author Replies Views Last Post
  HP Prime: complex numbers in CAS. Alberto Candel 1 1,864 12-06-2013, 02:36 PM
Last Post: parisse
  [HP Prime] Plots containing complex numbers bug? Chris Pem10 7 3,564 12-05-2013, 07:40 AM
Last Post: cyrille de Brébisson
  Prime: size display bug when editing large programs BruceH 2 1,314 10-31-2013, 05:30 PM
Last Post: BruceH
  HP Prime: How to use a large array in a program? HP Pioneer 2 1,387 10-27-2013, 03:15 AM
Last Post: steindid
  comparing numbers on the WP 34S Kiyoshi Akima 7 2,447 10-19-2013, 09:28 AM
Last Post: walter b
  HP Prime: Operations with Large Numbers Eddie W. Shore 0 938 10-19-2013, 12:24 AM
Last Post: Eddie W. Shore
  HHC 2013 room numbers David Hayden 2 1,280 09-20-2013, 05:34 PM
Last Post: sjthomas
  [HP-Prime xcas] operations with complex numbers + BUGs + Request CompSystems 9 3,377 09-08-2013, 10:40 PM
Last Post: CompSystems
  TED Talk: Adam Spencer: Why I fell in love with monster prime numbers Les Bell 3 1,688 09-05-2013, 12:54 PM
Last Post: Ken Shaw
  Irrationality in numbers....the book Matt Agajanian 4 1,796 08-30-2013, 04:14 PM
Last Post: Matt Agajanian

Forum Jump: