Re: Mersenne: Any statistics majors out there?

[Nicolau C. Saldanha]

On Sun, 9 May 1999, I wrote:

> Also, I would like to make sure I understand the arithmetic in the last
> paragraph. You say the FFT values contain 20 bits of data each and that
> they range from 2^19 to -2^19: I assume this means that they are
> integers with 19 digits base 2, plus one bit for the sign.
> But what are these integers? Surely not an instance of the Lucas-Lehmer
> sequence mod p, or they would have as many bits as p, which is around  
> 23 for the values of p being currently tested.

That was a stupid possibility, of course. It is the *exponents*
which have approx 23 bits and the LL sequence must be computed
modulo the *Mersenne number*, which has millions of bits.
But I still do not understand what exactly has 20 bits.
Perhaps a term of the LL sequence is written in base 2^20,
so that each "digit" is a block of 20 bits?

Nicolau

http://www.mat.puc-rio.br/~nicolau

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