Explore the sieve of eratosthenes and use it to find the prime no. less than 100
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When it comes to number envy, primes definitely steal the show, and for good reason. They’re fundamental, mysterious and hard to come by. They’re valuable for encryption and at the heart of some of the most elusive problems of history, the Riemann Hypothesis & Goldbach’s Conjecture.
So let’s get to know these numbers a little.
Definitions

the first 7 prime numbers
A number is prime if it has exactly two positive whole number divisors, one and itself.
A number is composite if it has more than two positive whole number divisors.
That means there exists numbers that are neither prime nor composite such as 0, 1 and any non-whole numbers.
Prime numbers are fascinating because there is no pattern or formula to predict them. The larger they get, the more difficult they are to find because the list of possible numbers they cannot be divided by grows. Needless to say, really large prime numbers are few and far between.
Currently, the largest known prime number was found in 2013 and is 17,425,170 digits long! The number is so big that it is recorded as:

Largest known prime number
Mathematicians call primes that are one less than a power of 2 (like the one above) Mersenne Primes, named after 17th century French mathematician, music theorist, and Minim Friar Marin Mersenne.
Discovering a new prime number is a noteworthy accomplishment and could even win you a small fortune. The Electronic Frontier Association promises to award $150k to the first person or group who discovers a prime number at least 100,000,000 digits long and $250k to the first person or group who discovers a prime number at least 1,000,000,000 digits.
How do we know primes this big even exist?
In the next lesson, I’ll show you how we know that there exists an infinite quantity of prime numbers. So stay tuned!
But first…
Let’s find the first 25 prime numbers. To do this we’ll use a technique pioneered by ancient Greek mathematician Eratosthenes.
(Note: If you have children, this is a great introductory exercise. See if you can help them figure out how to eliminate numbers to find the primes.)
The Sieve of Eratosthenes
To discover the first 25 prime numbers, we’ll sift out all the composite numbers between 1 and 100 using multiples.
Begin by listing out the numbers from 1 to 100.

Now erase all of the multiples of 2, except 2 itself.

Next erase all multiples of 3, 5 and 7, except for 3, 5 and 7 themselves.

There are no multiples of 11, 13, 17, 19, … left on the list. Finally remove 1 since it isn’t prime. What’s left is the first 25 prime numbers.

First 25 prime numbers
Thanks for reading!
Please click the ❤ to let me know you learned something new!
How Do We Know Prime Numbers are Infinite?
Euclid’s Theoremmedium.com
Generating Factors Using Prime Numbers
& The Fundamental Theorem of Arithmeticmedium.com
Why Does the Euclidean Algorithm Work?
(and the lock riddle solution)medium.com
Mathematics
Math
Tutorial
Prime Numbers
Number Theory
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Math Memoirs
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Responses
Conversation between Daniel and Brett Berry.

Daniel
Feb 6, 2016
Actually there is a formula to predict prime numbers. 1,2,3 aside you can predict them with the formula 6n+/-1
As said leaving 1,2 and 3 aside and also 6*0 where +/-1 one would be 1 and -1.
Next you take a look at 6*1 so 6.
Read more…
5
5 responses
So let’s get to know these numbers a little.
Definitions

the first 7 prime numbers
A number is prime if it has exactly two positive whole number divisors, one and itself.
A number is composite if it has more than two positive whole number divisors.
That means there exists numbers that are neither prime nor composite such as 0, 1 and any non-whole numbers.
Prime numbers are fascinating because there is no pattern or formula to predict them. The larger they get, the more difficult they are to find because the list of possible numbers they cannot be divided by grows. Needless to say, really large prime numbers are few and far between.
Currently, the largest known prime number was found in 2013 and is 17,425,170 digits long! The number is so big that it is recorded as:

Largest known prime number
Mathematicians call primes that are one less than a power of 2 (like the one above) Mersenne Primes, named after 17th century French mathematician, music theorist, and Minim Friar Marin Mersenne.
Discovering a new prime number is a noteworthy accomplishment and could even win you a small fortune. The Electronic Frontier Association promises to award $150k to the first person or group who discovers a prime number at least 100,000,000 digits long and $250k to the first person or group who discovers a prime number at least 1,000,000,000 digits.
How do we know primes this big even exist?
In the next lesson, I’ll show you how we know that there exists an infinite quantity of prime numbers. So stay tuned!
But first…
Let’s find the first 25 prime numbers. To do this we’ll use a technique pioneered by ancient Greek mathematician Eratosthenes.
(Note: If you have children, this is a great introductory exercise. See if you can help them figure out how to eliminate numbers to find the primes.)
The Sieve of Eratosthenes
To discover the first 25 prime numbers, we’ll sift out all the composite numbers between 1 and 100 using multiples.
Begin by listing out the numbers from 1 to 100.

Now erase all of the multiples of 2, except 2 itself.

Next erase all multiples of 3, 5 and 7, except for 3, 5 and 7 themselves.

There are no multiples of 11, 13, 17, 19, … left on the list. Finally remove 1 since it isn’t prime. What’s left is the first 25 prime numbers.

First 25 prime numbers
Thanks for reading!
Please click the ❤ to let me know you learned something new!
How Do We Know Prime Numbers are Infinite?
Euclid’s Theoremmedium.com
Generating Factors Using Prime Numbers
& The Fundamental Theorem of Arithmeticmedium.com
Why Does the Euclidean Algorithm Work?
(and the lock riddle solution)medium.com
Mathematics
Math
Tutorial
Prime Numbers
Number Theory
Like what you read? Give Brett Berry a round of applause.
From a quick cheer to a standing ovation, clap to show how much you enjoyed this story.
331
12
Follow

Brett Berry
❤ Lover of all things Math ❤
Follow

Math Memoirs
Tutorials with a fresh perspective.
More from Math Memoirs
Why Was 5 x 3 = 5 + 5 + 5 Marked Wrong

Brett Berry
4.92K
More from Math Memoirs
Common Core Math is Not the Enemy

Brett Berry
3.8K
More from Math Memoirs
A King, 1000 Bottles of Wine, 10 Prisoners and a Drop of Poison

Brett Berry
893
Responses
Conversation between Daniel and Brett Berry.

Daniel
Feb 6, 2016
Actually there is a formula to predict prime numbers. 1,2,3 aside you can predict them with the formula 6n+/-1
As said leaving 1,2 and 3 aside and also 6*0 where +/-1 one would be 1 and -1.
Next you take a look at 6*1 so 6.
Read more…
5
5 responses
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