Re: Mersenne: hi everyone

2001-11-19 Thread Daran 


- Original Message -
From: Nathan Russell [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Sunday, November 18, 2001 5:24 PM
Subject: Re: Mersenne: hi everyone

 I cannot help wondering if this is the sequence M(2), M(M(2)), M(M(M(2))),
 etc, which is indeed prime for all terms even vaguely capable of testing
 at the present time.

 The problem is that 90 digits in the exponent seems high for M(M(127)),
 the next term in the sequence.

My understanding is, that in the absence of any number-theoretical reason to
believe this sequence always prime (or otherwise to believe M(M(127))
prime), it's generally expected to be composite.

 Nathan

Daran G.


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Re: Mersenne: hi everyone

2001-11-18 Thread Daran 

- Original Message -

From: jowy [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Thursday, November 15, 2001 12:42 PM
Subject: Mersenne: hi everyone

 Hi

 I subscribed yesterday to the Mersenne mailing list. I'm a french student,
 and I'm very interested in mathematics and arithmetic. I worked with
friends
 on a sequence of number which we suppose to give only prime numbers.
 It works for the 6 first numbers of the sequence, but I grows very fast.
 The 7th would be a 90 digits exponent.

What do you mean by 90 digits exponant?  That your number has 10^90
digits?  That it has about 10^90 bits?

 Is there a way to test this number? With Lucas Lehmer? Gauss?

Given that the largest verified prime has about 10^6 digits, and that we are
currently testing numbers up to about 10^7 digits, I would be surprised if
there was a practical way to prove your number prime.  There may, however,
be a simple way to prove it composite, or otherwise to prove your sequence
not always prime, using algebraic or number-theoretical techniques.

In general, number theorists do not give much credence to conjectures of
primality based solely upon the values of the first few elements of a
sequence.

Regards

Daran G.


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