## Re: [PrimeNumbers] Probable 40th Mersenne

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• ... Ernst Mayer is doing a double-check that is expected to complete sometime around the 21st.
Message 1 of 9 , Jun 3, 2003
At 11:42 AM 6/3/2003 +0100, Jon Perry wrote:
>Still no new news at www.mersenne.org.

Ernst Mayer is doing a double-check that is expected to complete
sometime around the 21st.
• ... simply ... Perhaps you ve confused Mersenne primes with their associated perfect numbers. Exercise: How many proper divisors does the 39th perfect number
Message 2 of 9 , Jun 11, 2003
--- In primenumbers@yahoogroups.com, "Jon Perry" <perry@g...> wrote:
> Is it not relatively simple to double check whether prime or not -
simply
> add the divisors and see if the result is 2n?

Perhaps you've confused Mersenne primes with their associated perfect
numbers.

Exercise: How many proper divisors does the 39th perfect number have?
• Exercise: How many proper divisors does the 39th perfect number have? Impossible to say; http://www.mersenne.org/status.htm Jon Perry perry@globalnet.co.uk
Message 3 of 9 , Jun 11, 2003
'Exercise: How many proper divisors does the 39th perfect number have? '

Impossible to say;

http://www.mersenne.org/status.htm

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• ... Actually, it s impossible to say, but you won t find out why at that link... Nobody knows whether the 39th perfect number is even. Indeed, nobody knows
Message 4 of 9 , Jun 12, 2003
> 'Exercise: How many proper divisors does the 39th perfect number have? '
>
> Impossible to say;
>
> http://www.mersenne.org/status.htm

Actually, it's impossible to say, but you won't find out why at

Nobody knows whether the 39th perfect number is even. Indeed, nobody
knows whether the 19th perfect number is even.

It would be a safe conjecture that there are no odd perfect numbers,
but it hasn't been proven. I know that it has been proven that there
are no odd perfect numbers < 10^300, so certainly the first 12
perfect numbers are known with certainty.
• I was assuming the no odd perfect conjecture to be true, in the sense that you have assumed it to be false. In which case, it is impossible to say via the
Message 5 of 9 , Jun 12, 2003
I was assuming the 'no odd perfect' conjecture to be true, in the sense that
you have assumed it to be false. In which case, it is impossible to say via

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
From: Jack Brennen [mailto:jack@...]
Sent: 12 June 2003 08:14
Subject: Re: [PrimeNumbers] Re: Probable 40th Mersenne

> 'Exercise: How many proper divisors does the 39th perfect number have? '
>
> Impossible to say;
>
> http://www.mersenne.org/status.htm

Actually, it's impossible to say, but you won't find out why at

Nobody knows whether the 39th perfect number is even. Indeed, nobody
knows whether the 19th perfect number is even.

It would be a safe conjecture that there are no odd perfect numbers,
but it hasn't been proven. I know that it has been proven that there
are no odd perfect numbers < 10^300, so certainly the first 12
perfect numbers are known with certainty.

Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
The Prime Pages : http://www.primepages.org/

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
• --On Wednesday, June 11, 2003 8:36 PM +0000 cite13083 ... Perfect numbers are never prime - all prime numbers are deficient. This is a pretty stupid way to
Message 6 of 9 , Jun 12, 2003
--On Wednesday, June 11, 2003 8:36 PM +0000 cite13083
<cite13083@...> wrote:

> --- In primenumbers@yahoogroups.com, "Jon Perry" <perry@g...> wrote:
>> Is it not relatively simple to double check whether prime or not -
> simply
>> add the divisors and see if the result is 2n?
>
> Perhaps you've confused Mersenne primes with their associated perfect
> numbers.

Perfect numbers are never prime - all prime numbers are deficient. This is
a pretty stupid way to check for perfect prime numbers - especially since
it is likely that all perfect numbers are even, and with an exception even
numbers are not prime.

> Exercise: How many proper divisors does the 39th perfect number have?

I assume you are referring to the 39th known perfect number, which is the
39th, or possibly 40th or 41st, even perfect number. The number in
question is 2^13466916(2^13466917 - 1)

It has 13466917*2-1 proper divisors - we can have any number of factors of
2, from 0 to 13466916, either with or without the megaprime. Note that
when we have no 2's, and no megaprime, we have the perfectly valid divisor
of 1. When we have all possible factors, we have the number itself, thus
the -1.

As a simpler illustration, take the perfect number 2^2*(2^3-1). It has 2
proper divisors with and 3 without the prime
2^3-1 - respectively, 1, 2, 4 and 7, 14. Thus the total is 2*3-1 - again,
1 less than twice the original exponent.

Is this correct?

Nathan
• ... It is very easy to say about the 39th largest one currently known.
Message 7 of 9 , Jun 12, 2003
At 03:33 AM 6/12/2003, Jon Perry wrote:
>I was assuming the 'no odd perfect' conjecture to be true, in the sense that
>you have assumed it to be false. In which case, it is impossible to say via