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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'

I'm not crazy, my mother had me tested.

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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)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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Thanks

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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'

I'm not crazy, my mother had me tested.

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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'

I'm not crazy, my mother had me tested.

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**yazz****Member**- Registered: 2014-01-14
- Posts: 425

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**