Whilst I was surfing I came across the word "Mersenne",
even though I didn't search for it.
After I had finished laughing, I had to tell you people.

The Hack Furby Challenge is a $250 prize offered by
Peter van der Linden http://www.afu.com/fur.html for
software to do something with a Furby. The original
Hack Furby Challenge was won by Jeffrey Gibbons who
supplied a Furby Upgrade Kit hardware, the new prize is
for software.

Peter van der Linden suggests "You can program Furby to solve
mathematical puzzles and equations, to look for Mersenne prime
numbers, or simply to act as a speaking clock."

The $74 upgrade,
http://www.appspec.net/products/UpgradeKits/FurbyUpgrade/root.html
replaces the original 6502 CPU with a 20MHz 8051 with 1MByte
of serial Flash RAM and 1152 bytes of normally accessible RAM.

Clearly this is not enough to Lucas-Lehmer test big Mersennes,
but it is enough to Reverse Factor 3072 bit factors upto
3072 bit exponents given a prime as an input.

As Reverse Factoring (without factoring P-1) is asymptotically
more productive at completely factoring any of all 2^N-1
compared with LL testing just prime exponents this shouldn't
be a problem given enough batteries and patience.

I will post my analysis of Reverse Factoring shortly.

Paul Landon


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