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#1 2013-04-21 02:59:56

Agnishom
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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 23:47:02

Agnishom
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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 =p1p2p3pn +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 dont add 1.

Last edited by Agnishom (2013-04-21 23:47:53)


'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'
'Who are you to judge everything?' -Alokananda
 

#3 2013-12-11 13:19:17

Agnishom
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Re: Prime Numbers

http://img.spikedmath.com/comics/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'
'Who are you to judge everything?' -Alokananda
 

#4 2013-12-11 20:43:08

Nehushtan
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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 dont add 1.

This proof is valid and correct.


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#5 2013-12-11 23:50:58

Agnishom
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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'
'Who are you to judge everything?' -Alokananda
 

#6 2013-12-12 10:02:04

ShivamS
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Re: Prime Numbers

It's not really a joke.


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Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann
 

#7 2013-12-12 11:59:16

Agnishom
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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'
'Who are you to judge everything?' -Alokananda
 

#8 2013-12-13 02:50:42

Nehushtan
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Re: Prime Numbers

Because its not funny. (#1 and #3 are funny; #2 isnt.)

Last edited by Nehushtan (2013-12-13 02:54:53)


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#9 2013-12-13 11:57:58

Agnishom
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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'
'Who are you to judge everything?' -Alokananda
 

#10 2014-01-25 02:42:20

yazz
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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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