What kind of Linux is this?

I'm running a copy of the Fedora 9 (Sulphur) which is bundled in this month's DVD. I want to install

1. Java Development Kit 6 Update 6 for developing Java programs ( & running out of time )

My CPU is an AMD Athlon 64 X2 3600+ [Dual-Core] [64-bit]

I went to sun's website to download jdk, it gives either an i586 (OR) x64 version. I don't know which version to download.........Because the System Info in fedora 9 shows that my copy is i686.........What is i686?.........whats the diff between i586 & i686 & x86-64?...........My CPU is an x86-64 Arch right?.........Is i686 32-bit or 64-bit?..........

Which version should i download?

And what is the convention used for a:

1.32-bit Version of Linux
2.64-bit Version of Linux

plz HELP I'm TEARING MY HAIR OUT...................