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#1 2013-04-20 04:59:56

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Prime Numbers

Statement All Prime numbers are odd

Proof
Lemma: A prime number greater than 2 is odd.
Proof: Assume the contrary, then 2 divides the number therefore it is not prime.

Now,
1. All prime numbers greater than 2 are odd
2. 2 is the only even prime number. Therefore, it is the oddest.

From 1 and 2, all prime numbers are odd


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#2 2013-04-21 01:47:02

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: Prime Numbers

Statement There are infinitely many prime numbers

Proof
Suppose that p1,p2,...,pn are n distinct primes. We construct a
prime pn+1 not equal to any of p1, . . . , pn, as follows. If
N =p1p2p3···pn +1
then there is a factorization N = q1q2 ···qm
with each qi prime and m≥1. If q1 =pi for some i,then pi |N. We also have pi |N−1, so pi |1=N−(N−1),which is a contradiction. Thus the prime pn+1 = q1 is not in the list p1, . . . , pn, and we have constructed our new prime.

Statement There are infinitely many composites.

Proof: To obtain a new composite number, multiply together the first n composite numbers and don’t add 1.

Last edited by Agnishom (2013-04-21 01:47:53)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#3 2013-12-10 14:19:17

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
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Re: Prime Numbers

370-lolproof.png


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#4 2013-12-10 21:43:08

Nehushtan
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From: London
Registered: 2013-03-09
Posts: 615
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Re: Prime Numbers

Agnishom wrote:

Statement There are infinitely many composites.

Proof: To obtain a new composite number, multiply together the first n composite numbers and don’t add 1.

This proof is valid and correct.


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#5 2013-12-11 00:50:58

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
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Re: Prime Numbers

Thanks smile


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2013-12-11 11:02:04

ShivamS
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Registered: 2011-02-07
Posts: 3,555

Re: Prime Numbers

It's not really a joke.

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#7 2013-12-11 12:59:16

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
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Re: Prime Numbers

Why not?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#8 2013-12-12 03:50:42

Nehushtan
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From: London
Registered: 2013-03-09
Posts: 615
Website

Re: Prime Numbers

Because it’s not funny. (#1 and #3 are funny; #2 isn’t.)

Last edited by Nehushtan (2013-12-12 03:54:53)


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#9 2013-12-12 12:57:58

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
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Re: Prime Numbers

Is not funny because it is valid?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#10 2014-01-24 03:42:20

yazz
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Registered: 2014-01-14
Posts: 412

Re: Prime Numbers

it would be really funny when we talk about these in classes when the chapters are going very seriously.


Knowledge is knowing that a tomato is a
fruit, but Wisdom is knowing not to put it in a fruit salad tongue.

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