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**Prime Numbers**

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** 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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**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 dont 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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'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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Agnishom wrote:

StatementThere 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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Thanks

'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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,610

It's not really a joke.

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Why not?

'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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Is not funny because it is valid?

'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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**yazz****Member**- Registered: 2014-01-14
- Posts: 422

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 .

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**Prime Numbers**