Thanks again to everyone for their help!
Paul Goracke, among others, suggested that "Developer Tools" might be
in my "/Applications/Installers/" directory. I had even started to
download "Developer Tools" from ADC (Apple had got my registration
straightened out) when I realized that Paul was right---so I
cancelled the transmission.
It's kind of pathetic. I spent most of an hour on two phone calls to
Apple Technical Support yesterday. Both people I talked to were iMac
specialists, presumably, but there was a good deal of wait time while
they asked even more expert technicians for advice. Still, no one at
Apple had the slightest notion that Developers Tools was already
loaded, ready to be installed, on my new iMac's hard drive.
In any case, I've now installed the Developers Tools and CPAN. I've
even installed Steffen Beyer's "Bit:Vector" to run a comparison
against my Power Computing, 240 MHz PowerPC 604e machine.
So here is the answer to your homework exercise. There is exactly one
nonsquare multiple of 4 less than or equal to 10,000,000 that is not
the sum of a square and a prime. That nonsquare multiple of 4 is
3,676.
Note that all small, nonsquare multiples of 4 do have a square plus
prime decomposition:
8 = 1 + 7, 12 = 1 + 11, 20 = 1 + 19 = 9 + 11,
24 = 1 + 23, 28 = 9 + 19 = 25 + 3, ...
The exercise with the 10,000,000 upper limit took 26 minutes and 53
seconds on my new iMac. I don't think I'll try it on my Power
Computing tower. When I set the upper limit at 2,000,000 rather than
10,000,000, the comparative computation times were
Power Computing 240 MHz: 8 minutes, 43 seconds,
iMac 800 MHz: 2 minutes, 53 seconds.
So far, no matter which machine I use, the answer is always the same: 3,676.
Regards,
Vic
--
*---* mailto:vic@;norton.name
| Victor Thane Norton, Jr.
| Mathematician and Motorcyclist
| phone: 419-353-3399
*---* http://vic.norton.name
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