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# Maths Project- Euclid Prime Numbers

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## Ber Ber

on 23 October 2013

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#### Transcript of Maths Project- Euclid Prime Numbers

Personal Information-
Euclid
is known
as "The Father
of Geometry"
Euclid was born in 300 BC.
Euclid pronounced YOOdclud (Greek: Eukleides of Alexandria, Egypt)
People often confused Euclid with the philosopher Eukleides of Megara
Euclid was the most famous mathematician with Greco-Roman antiquity. Some say that Euclid was older than Archimedes but it cannot be confirmed because his birth date and death circumstances are unknown. He is best known for his geometry results. Euclid's influence was probably Plato as Euclid attended Plato's Academy.
Prime numbers were first studied by the ancient Greeks. Here's another unique quirk about prime numbers: it's incredibly hard to predict – there's no formula for figuring out what the next largest prime number is.
So before computers, mathematicians used something called the Sieve of Eratosthenes to spot prime numbers in a simple range (of say, 1-100).
Sieve of Eratosthenes
Applying Strategies
•If the sum of a number's digits is a multiple of 3, that number can be divided by 3.
•No prime number greater than 5 ends in a 5. Any number greater than 5 that ends in a 5 can be divided by 5.
•2 and 5 are the only prime numbers that end with a 2 or a 5.
•The largest prime number known has around 13 million digits!
Here are some fun facts about prime numbers:
Explaining
This means that no matter how many primes exist, there must be at least one more. So that means the number of primes is infinite. This is a contradiction to the original theory, so the assumption that there are a finite number of primes is hereby
Euclid
Euclid's Process
Daily Uses of
rime Numbers
Prime Security
Prime Numbers in Nature
Prime numbers may also play a role in the periodical cicada's life cycle, which spans 13 or 17 years. That those two are prime numbers isn't a coincidence, scientists say.

Prime Numbers-
Euclid

Euclid's Theorem- Prime Numbers
Theorem

Questioning
These are some of the questions

that Euclid asked to himself when he was working on prime numbers and what the next prime number was:
Communicating
Reasoning
Hands on activity
Step 1
= prime

Step 2
= "the last prime number"

If...
...
and
...
then
Prime numbers play a key role in internet security. They are used for many codes. Without prime numbers, it would be easy for hackers to steal important information such as passwords, credit card numbers, and bank account numbers.
Note:
There are infinitely many primes.
Example- 2, 3 and 5.

2 x 3 x 5 = 30
30 + 1 = 31
31 is a prime number
HMMM...
What are prime numbers
Prime numbers are numbers that have two factors. The factors are the number 1 and the number itself. For example the number 2 is a prime number because it can only be divided by 2 which is the number itself and the number 1.
Question:
Why are prime numbers called primes?
Two thousand years ago, Euclid wrote in his book, The Elements that
'prime numbers are that unit alone measured'.
Translated-
A prime number is that which is divided by a unit alone.
But why "prime"?
The Greek philosophers used the word 'prôtos' as the sense of first in order of existence. 'Prôtos' is one of the standard meanings of our "prime" or "primary".
All other numbers (positive integers) are measured by primes but primes alone are measured only by units. This makes prime numbers first.
In 1570 sir Henry Billingsley first translated Euclid's Elements into English, forever establishing "prime" as the correct English term for prime numbers. This translation was noted as the first and most important translation into English.
In summary: we use the English word prime because the ancient Greeks saw them as multiplicative first, so Billingsley translated Euclid's 'prôtos' as 'prime'.

Step 3
(Proof)
Why are there only a finite amount of prime numbers?
What makes a prime number so difficult to find and predict?
Why isn't there a formula to find out what the next prime number was?
Did any other mathematician try to figure out what the next prime number is before I did?
Why do we have numbers that are called prime numbers in our number system?
Why are prime numbers called prime numbers?

P1
N
N
What is a prime number?
How do you find prime numbers?
Why are the prime numbers so unpredictable?
Is there any way of predicting prime numbers?
Are prime numbers finite or infinite?
How can I prove that prime numbers are infinite?
Is there a formula about prime numbers?
Hands on Activity
P1
N
N
45 second quiz on prime numbers
HAVE FUN!
This song explains that first there were a finite amount of primes (Three little primes), then they ran out or 'left' (And no
little primes came back). But then mother prime discovers that primes
are infinite due to the formula 'P1XP2...The last prime+1= Another prime'. This song also lists a few prime numbers.
Song- Three little ducks- The Prime Version
How do we communicate it?

1. Three little primes
Went out one day
Over the hill and far away
Mother prime said
"1, 3, 5, 7."
But only two little primes came back.

Went out one day
Over the hill and far away
"2,3,5."
And an infinite amount of primes came back.
3. One little prime
Went out one day
Over the hill and far away
Mother prime said
"2, 3, 5, 7."
But none of the five little primes came back.
2. Two little primes
Went out one day
Over the hill and far away
Mother prime said
"2, 3, 5, 7."
But only one little prime came back.
I
M
A
G
I
N
E

I
F
.
.
.
Theory 1
There are finte amount of prime numbers.
Theory 2
There are a infinte amount of prime numbers.
.
Cute but clever right?

Trees are smart!
I'm innocent!!!!
By Ashitha "the buji buji" and Jessica "the innocent"

How he communicated it

Can you guess the first?
Euclid's influence on mathematics
Euclid's work was recorded in his book called "The Elements". The Elements is the most influential and non-religious book of all time and the most famous axiomatic system book in the world. It was the second most printed book.
Euclid’s work was studied by Greek and Roman scholars for a thousand years. It was
then translated to Arabic around 800 A.D. and studied by Arab scholars too.
...but not as innocent as us!
Sir Buji the detective is here!
Instructions- Answer the questions and once you are finished, shout out
“Ashitha and Jessica’s Presentation was the best!”