Well, you are right Lucas.  So we'll tell ET that's how we did it. :-)
Boy, will we get credit for being smart !

At 04:21 PM 6/15/99 -0400, you wrote:
>>I was thinking about this last night. If you could keep track of the
>>divisions for the last Mersenne, you could keep that as a starting point. So
>>for example, take M37, and keep track of how many times you did your modulo
>>and what the divisor was. Then you could conceptually get back to what
>>S(M37) was w/o the modulo by multiplying M37*(sum of divisors) or something
>>along those lines. It would at least save you some time, sure there's a big
>>modulo calculation in the beginning, and I'm sure the number is friggin'
>>huge, but it can be represented as (2^p-1)*(some number).
>
>Well, friggin' huge doesn't even begin to describe it.  There aren't enough
>quanta in the universe to hold it.  With each sqaring, it aproximatly 
>doubles the number of binary digits, so that number would be aproximatley
>2^(2^(p-1)) binary digits long (probably way off by a factor of 2^1000000, 
>or something, but when it gets that big, that doesn't matter).
>
>-Lucas Wiman

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