Largest known k? - Page 4

henryzz · 2009-07-13, 16:42

Quote:

Originally Posted by 10metreh

1 is the smallest factor of any whole number.

it is not the smallest prime factor however

10metreh · 2009-07-13, 16:54

Quote:

Originally Posted by henryzz

it is not the smallest prime factor however

Yes, but the gang were talking about the "smallest factor of a number". This is actually 1, but they were using it as the "smallest prime factor".

I notice that my posts in threads that are not in the Factoring Projects superforum often have the effect of drastically reducing the posting rate in that thread. What is the reason for this?

Oh yes, and I have guessed what everyone's reactions will be

TimSorbet · 2009-07-13, 17:10

Of course, trivially every natural number over 1 has at least two factors: 1 and itself. With Mersenne numbers these correspond to k=0 and k=(Mp-1)/2p, respectively. But it makes sense to restrict our search to k's such that 0<k<(Mp-1)/2p.
Saying that 1 and Mp qualify just because we didn't specify prime factor is just being pedantic, and you know it.

cheesehead · 2009-07-13, 21:51

Quote:

Originally Posted by 10metreh

I notice that my posts in threads that are not in the Factoring Projects superforum often have the effect of drastically reducing the posting rate in that thread. What is the reason for this?

Correlation is not causation. Maybe you're just habitually late to get into the discussions outside Factoring Projects. :-)

MatWur-S530113 · 2009-07-17, 02:52

Quote:

Originally Posted by plandon

The biggest known smallest k is (M42643801-1)/(2*42643801)

This thread is interesting.
What is the average k? How often is k=1?
or where is the data so that I can average it myself?

A factor of a Mersennenumber has k=1 if and only if the prime exponent p is a Sophie Germain prime (then 2p+1 is prime, too) congruent 3 mod 4.

It is not known wheather there are infinity many SG primes or not.

best regards,

Matthias

Uncwilly · 2009-07-17, 05:39

Quote:

Originally Posted by MatWur-S530113

A factor of a Mersennenumber has k=1 if and only if the prime exponent p is a Sophie Germain prime (then 2p+1 is prime, too) congruent 3 mod 4.

In the range of 332192831 - 332399999 there are 347 with k=1.

2009-07-13, 17:10	#36
TimSorbet Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 11·389 Posts	Of course, trivially every natural number over 1 has at least two factors: 1 and itself. With Mersenne numbers these correspond to k=0 and k=(Mp-1)/2p, respectively. But it makes sense to restrict our search to k's such that 0<k<(Mp-1)/2p. Saying that 1 and Mp qualify just because we didn't specify prime factor is just being pedantic, and you know it. Last fiddled with by TimSorbet on 2009-07-13 at 17:12 Reason: "every number has" > "every natural number over 1 has" so as to avoid any more pedantry :)

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