Mathematicians Make a Major Discovery About Prime Numbers

heckler73 said:

Paul Erdos...
Rather appropriate, actually.

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TBoneJack said:

Yes. He was amazing, wasn't he?

As a young math major in the mid 1980s, I was very interested in prime number theory. And at that same time, a 10-year-old prodigy was being schooled by a patient Paul Erdos. And that prodigy is the one responsible for the recent breakthrough.

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Amazing? That's an understatement.
Amped-up is more what I was thinking
So I guess you know how many people one needs to invite to a dinner party to guarantee at least 3 people know each other or do not know each other.

heckler73 said:

Amazing? That's an understatement.
Amped-up is more what I was thinking
So I guess you know how many people one needs to invite to a dinner party to guarantee at least 3 people know each other or do not know each other.

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TBoneJack said:

Not off the top of my head. But I know how many people it takes for there to be an expectation of a birthday (month and day) match.

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Seriously...if you like Tao and Erdos, that book will "amaze" you It was the strangest "textbook" I have ever read, and one I need to revisit. Part textbook on Ramsey Theory and combinatorics, part history, part treasure hunt (lots of unsolved problems with prizes in there).

heckler73 said:

Oh!
You would probably like this book:

Seriously...if you like Tao and Erdos, that book will "amaze" you It was the strangest "textbook" I have ever read, and one I need to revisit. Part textbook on Ramsey Theory and combinatorics, part history, part treasure hunt (lots of unsolved problems with prizes in there).

This is a good journal on the field:
http://www.integers-ejcnt.org/

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TBoneJack said:

Not off the top of my head. But I know how many people it takes for there to be an expectation of a birthday (month and day) match.

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Moebius said:

How many? ..
30?

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TBoneJack said:

When the group has 23 people, the probably of a birthdate match (month and day) is 50%. At 30 people it's about 70%. At 70 people it's almost 100%.

n p(n)
5 2.7%
10 11.7%
20 41.1%
23 50.7%
30 70.6%
40 89.1%
50 97.0%
60 99.4%
70 99.9%
100 99.99997%
200 99.9999999999999999999999999998%
300 (100 − (6×10−80))%
350 (100 − (3×10−129))%
365 (100 − (1.45×10−155))%
366 100%

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TBoneJack said:

http://en.wikipedia.org/wiki/Birthday_problem

When the group has 23 people, the probably of a birthdate match (month and day) is 50%. At 30 people it's about 70%. At 70 people it's almost 100%.

n p(n)
5 2.7%
10 11.7%
20 41.1%
23 50.7%
30 70.6%
40 89.1%
50 97.0%
60 99.4%
70 99.9%
100 99.99997%
200 99.9999999999999999999999999998%
300 (100 − (6×10−80))%
350 (100 − (3×10−129))%
365 (100 − (1.45×10−155))%
366 100%

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Moebius said:

The problem with that question is what does 'expectation' mean and how do we objectively measure that.? What is expected by one person may not be expected by someone else. ... so the question as you have phrased it does not 'strictly' have a relation to that table of mathematical probability.

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TBoneJack said:

The terms "probability", "expectation", and "liklihood" are often used somewhat interchangeably in math talk.

As in "50% probability", "you can expect 50 of 100", or "50% liklihood".
"If you buy a lottery ticket every hour of every day forever, you could expect to win once every 300 years".

Things like that. But strictly speaking, you're probably (no pun intended) right that "probability" is the best choice of words to use.

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Moebius said:

In the


But youre mistaking the term 'probability' in math with the subjective notion of human 'expectation'. They're two completely different things and have been shown so in numerous scientific experiments.


EDIT:
sorry I missed your last sentence. ..I think you understood my point.

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TBoneJack said:

Although not as straightforward as the term "probability", the term "expectation" is an objective mathematical term that is used in probability theory and statistics.

http://mathworld.wolfram.com/ExpectationValue.html

Probability is a term that is equally applicable to one event, or multiple events. For instance, the probability that you will draw a blue ball out of a basket that contains 4 red balls and one blue ball is 20%. But what can you expect? I'm not sure.

But if you repeat that same draw 100,000,000 times (resetting the basket after each draw), you can expect to draw a blue ball 0.20 * 100,000,000 = 20,000,000 times.

Not exactly, I know. But the probability density function is at its peak at 20,000,000 times. And expectation is defined in terms of the probability density function.

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TBoneJack said:

Although not as straightforward as the term "probability", the term "expectation" is an objective mathematical term that is used in probability theory and statistics.

http://mathworld.wolfram.com/ExpectationValue.html

Probability is a term that is equally applicable to one event, or multiple events. For instance, the probability that you will draw a blue ball out of a basket that contains 4 red balls and one blue ball is 20%. But what can you expect? I'm not sure.

But if you repeat that same draw 100,000,000 times (resetting the basket after each draw), you can expect to draw a blue ball 0.20 * 100,000,000 = 20,000,000 times.

Not exactly, I know. But the probability density function is at its peak at 20,000,000 times. And expectation is defined in terms of the probability density function.

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Moebius said:

Nothing to do with your original mathematical conundrum. terrible. I'm out.

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