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Old 2010-02-15, 08:03   #1
10metreh
 
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Nov 2008

44228 Posts
Default A new driver? (or type of driver?)

2^8 * 7 * 73 is a guide. According to the rules, it is class 4, so it isn't too hard to escape.
However, if you add in a 5, a 19 and a 37 to produce 2^8 * 5 * 7 * 19 * 37 * 73, then the 2^8 keeps the 7 and the 73 there, the 19 keeps the 5 there, the 37 keeps the 19 there and the 73 keeps the 37 there. The main difference is that the new primes raise the power of 2 of the sigma to 8, and other prime factors will raise it to 9 or more, meaning that it will keep the 2^8.
As far as I can see, you can only escape this structure when one of the factors in it is squared (like a driver that isn't 2^3 * 3 or the downdriver), but according to Clifford Stern's page (linked above), the guide is just the 2^8 * 7 * 73. The original definition of drivers and guides only allows for drivers formed from factors of the sigma of the power of 2, but clearly other primes can have a huge effect.

I apologise if this is incorrect.

Last fiddled with by 10metreh on 2010-02-15 at 08:04
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