> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] 


> 
> (Aside - we're rather more likely to find a 75-bit factor than a 75-
> digit factor. In fact, finding a 75-digit prime factor of a 
> "no factors 
> known" Mersenne number with an exponent under 80 million would 
> be a significant achievement in itself.

Finding a 75-digit prime and non-algebraic factor of any integer with
more than, say, 200 digits would be a significant achievement.  The
record today is 55 digits; it reached 53 digits 3 years ago and only a
handful of factors with 50 or more digits have been found ever.  I have
precisely one of them to my credit 8-)

> At the moment, having found one factor, we quit. That's sufficient 
> effort for the purpose of trying to find Mersenne primes. A little 
> more work might break the cofactor down further.

Actually, some of us don't quit.  But we're a small bunch of weirdos,
and we only work on tiny exponents anyway.


Paul
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