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From: jpser@cup.portal.com (John Paul Serafin)
Newsgroups: comp.sys.handhelds,sci.math.symbolic
Subject: HP48/Kalb/Bos dusts 80486/Mathematica
Message-ID: <43391@cup.portal.com>
Date: 17 Jun 91 02:33:18 GMT
Organization: The Portal System (TM)
Lines: 56

I have stumbled across several integers which are factored by the ultimate 
prime factor routines for the HP48 by Klaus Kalb and Jurjen Bos much
faster than Mathematica 1.2 running on a 25MHz 486.   There were also
some integers which took 9 to 15 seconds on both machines.   Because i/o
is so slow on the HP48, Mathematica is much faster on easy to factor
integers, but the 48 is so fast, it really doesn't matter.   There are
many things which Mathematica can do and the HP48 can not, and in general
Mathematica is much faster.   Nonetheless, I think these results say
some things about both the HP48 and Mathematica.   (The "no math coprocessor 
required" version of Mathematica was used, but I doubt that floating point 
numbers are involved).   I found these integers several weeks ago, but it 
looks like I won't have time to do a good job of studying or documenting 
any time soon.  So, here are some of my results.
----------------------------------------------------------------------------
Number                          HP48 time     Mathematica time (MSDOS 80486)
4,611,686,018,427,387,903
= 2^62 - 1                      508 sec       After more than 8 hours and
                                              less than 20 hours, Mathematica
                                              ran out of memory. (5M extended,
                                              8M RAM swap disk.   This case
                                              was rerun with 12M extended
                                              memory and 60M free space on a
                                              fixed disk as swap space.
                                              After nearly two days, the
                                              problem was still running. The
                                              run was aborted and MaxMemory
                                              Used returned 43,761,628. The
                                              HP48 had less than 6000 bytes
                                              free at the start of the run.
128,573,131,101,428,317
= 573,259,391 *                 241 sec       After more than 8 hours, etc.
  224,284,387                                 This was before trying hard
= 30,000,000th prime *                        swap and 12M main memory.
  12,345,678th prime
            
50,303,624,411,148,161          151 sec       "
= 224,284,387 *
  224,285,003

5,260,991,541,853,343            45 sec       I killed this one, too.  Not
= 224,284,387 *                               sure when, but much longer
   23,456,789                                 than 45 seconds.
           
The last is smallest number I have found so far that sends Mathematica out 
to lunch.   The largest number the HP48 can factor with the Kalb/Bos routine 
is 2^64 -1.
Mathematica documentation states that Mathematica will factor a number
with fewer than 25 digits almost immediately (page 84 of the second
edition, page 554 says integers less than 20 digits should give no
problem.
I would be interested in knowing how Mathematica does with the above
numbers on other computers, perhaps with more memory, what the smallest
"pathological" integer for Mathematica is, and whether there are any
integers that take Mathematica more than 5 minutes and less than an hour.
John Serafin
jpser@cup.portal.com