A real GIMPS math thought - Page 2

davieddy · 2011-05-29, 19:30

Quote:

Originally Posted by cheesehead

Okay. You're right. My intuition failed me there. I'll try to remember.

Likewise, I think my original "thought" was probably wrong.

Since the elimination of candidates by factoring goes hand in hand
with increased probability of the surviving ones being prime, I think
I was "double counting" two ways of viewing the same thing.

Still not sure yet though.

David

davieddy · 2011-05-31, 00:55

Is there a simple explanation or even definition of Euler's gamma?
OK I know Google is my friend, but I have a feeling William or
such might quicken my understanding more succinctly.

David

cheesehead · 2011-05-31, 01:13

Quote:

Originally Posted by davieddy

Is there a simple explanation or even definition of Euler's gamma?
OK I know Google is my friend, but I have a feeling William or
such might quicken my understanding more succinctly.

David

MathWorld is an especially mathematical friend.

From http://mathworld.wolfram.com/ a search on "Euler's gamma" produces a list on which one eventually finds http://mathworld.wolfram.com/Euler-M...iConstant.html

Whether you find the explanation there succinct, I don't know. But note that gamma is not as simple as other well-known constants; it is not yet known even whether it is rational or irrational!

science_man_88 · 2011-05-31, 01:15

Quote:

Originally Posted by davieddy

Is there a simple explanation or even definition of Euler's gamma?
OK I know Google is my friend, but I have a feeling William or
such might quicken my understanding more succinctly.

David

well if you just want the value:

Code:

Euler

is the way in PARI.

it appears in Google as the Euler-Mascheroni constant.

davieddy · 2011-05-31, 15:21

Quote:

Originally Posted by cheesehead

it is not yet known even whether it is rational or irrational!

Two thoughts on that one.

1) If it was rational, you would think the fact would be known by now

2) Didn't Cantor work out that there were more irrational numbers than rational ones?

Shall we have a wager on the likeliest answer to this question?

David

davieddy · 2011-05-31, 16:38

Quote:

Originally Posted by davieddy

Two thoughts on that one.

1) If it was rational, you would think the fact would be known by now

2) Didn't Cantor work out that there were more irrational numbers than rational ones?

Shall we have a wager on the likeliest answer to this question?

David

I'll offer you Aleph0 to Aleph1

(Not surprised Georg Cantor went a bit mad!)

cheesehead · 2011-05-31, 17:15

Quote:

Originally Posted by davieddy

Two thoughts on that one.

1) If it was rational, you would think the fact would be known by now

(1960) If no map requires five colors, you'd think we would have a proof by now.

If Fermat's Last Theorem were true, you'd think ...

science_man_88 · 2011-05-31, 17:27

Quote:

Originally Posted by cheesehead

(1960) If no map requires five colors, you'd think we would have a proof by now.

If Fermat's Last Theorem were true, you'd think ...

has anyone tried to turn the sum into anything because since n doesn't change in the sum part as far as I know , the -ln n can be turned into -n ln n and taken out of the sum so then it's up to defining the sum of the 1/k for k=1-> n the simplest form I can figure is something $\frac{x}{n!}$ where I haven't solved for x.

science_man_88 · 2011-05-31, 17:31

Quote:

Originally Posted by science_man_88

has anyone tried to turn the sum into anything because since n doesn't change in the sum part as far as I know , the -ln n can be turned into -n ln n and taken out of the sum so then it's up to defining the sum of the 1/k for k=1-> n the simplest form I can figure is something $\frac{x}{n!}$ where I haven't solved for x.

figured out the sum wrong doh. though the formula using the harmonic numbers ( which are fractions make it seem that asking about rationality is asking if ln n can be expressed as a fraction at the limit.

davieddy · 2011-05-31, 21:16

Quote:

Originally Posted by cheesehead

(1960) If no map requires five colors, you'd think we would have a proof by now.

Son of our erstwhile pipe-smoking prime minister, I am sure you will enjoy
Robin Wilson's book "The four colour theorem"

As I have probably mentioned before, I am fortunate enough to
have been great friends with Paul Seymour

David

Christenson · 2011-05-31, 23:53

Quote:

Originally Posted by davieddy

I'll offer you Aleph0 to Aleph1

(Not surprised Georg Cantor went a bit mad!)

I'll wager the number between Aleph0 and 2^Aleph0.....the standard conjecture is that gamma its transcendental....

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2011-05-31, 00:55	#13
davieddy "Lucan" Dec 2006 England 2×3×13×83 Posts	Is there a simple explanation or even definition of Euler's gamma? OK I know Google is my friend, but I have a feeling William or such might quicken my understanding more succinctly. David