Prime numbers are natural numbers that are divisible by only 1 and the number itself. In other words, prime numbers are positive integers greater than 1 with exactly two factors, 1 and the number itself. Some of the prime numbers include 2, 3, 5, 7, 11, 13, etc. Always remember that 1 is neither prime nor composite. Also, we can say that except for 1, the remaining numbers are classified as prime and composite numbers. All prime numbers are odd numbers except 2, 2 is the smallest prime number and is the only even prime number. [1]
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“Prime numbers are the very atoms of arithmetic… The primes are the jewels studded throughout the vast expanse of the infinite universe of numbers that mathematicians have studied down the centuries.”
Marcus du Sautoy, The Music of the Primes
References
[1] “Prime Numbers – Definition, Chart, Prime Numbers 1 to 1000, Examples.” 2022. BYJUS. BYJU’S. December 23. https://byjus.com/maths/prime-numbers/.
Kiger, Patrick J. 2023. “What Are Prime Numbers, and Why Do They Matter?” HowStuffWorks Science. HowStuffWorks. November 30. https://science.howstuffworks.com/math-concepts/prime-numbers.htm.
Lamb, Evelyn. 2024. “Why Isn’t 1 a Prime Number?” Scientific American. February 20. https://www.scientificamerican.com/blog/roots-of-unity/why-isnt-1-a-prime-number/.
PRIMES AND PRIME FACTORISATION. 2021. The Improving Mathematics Education in Schools (TIMES) Project. Accessed March 6. https://amsi.org.au/teacher_modules/Primes_and_Prime_Factorisation.html.
Additional Reading
Agramunt-Puig, Sebastia. 2020. “Prime Numbers.” Medium. Medium. October 10. https://sebastiaagramunt.medium.com/prime-numbers-7eab54534809.
Prime numbers are the building blocks of arithmetics. In this short post we will investigate some attributes of prime numbers and how to work with them in a computer.
Honner, Patrick. “How Can Infinitely Many Primes Be Infinitely Far Apart?” Quanta Magazine, July 21, 2022. https://www.quantamagazine.org/how-can-infinitely-many-primes-be-infinitely-far-apart-20220721/.
Mathematicians have been studying the distribution of prime numbers for thousands of years. Recent results about a curious kind of prime offer a new take on how spread out they can be.
“Prime Factorization Calculator.” 2023. CalculatorSoup. October 20. https://www.calculatorsoup.com/calculators/math/prime-factors.php.
Use this prime numbers calculator to find all prime factors of a given integer number up to 10 trillion. This calculator presents:
1. Prime factors of a number
2. Prime decomposition in exponential form
3. CSV (comma separated values) list of prime factors
4. Factorization in a prime factors tree
For the first 5000 prime numbers, this calculator indicates the index of the prime number. The nth prime number is denoted as Prime[n], so Prime[1] = 2, Prime[2] = 3, Prime[3] = 5, and so on.
The limit on the input number to factor is less than 10,000,000,000,000 (less than 10 trillion or a maximum of 13 digits).
“Prime Number: Prime Time: Multiples and the World of Primes.” 2023. FasterCapital. Accessed March 6, 2024. https://fastercapital.com/content/Prime-Number–Prime-Time–Multiples-and-the-World-of-Primes.html.
Prime numbers are a fascinating concept in mathematics that have intrigued mathematicians for centuries. These special numbers have unique properties that set them apart from other integers. From a historical perspective, prime numbers have played a significant role in the development of number theory and cryptography. From a practical standpoint, they find applications in various fields, including computer science, data encryption, and prime factorization algorithms. In this section, we will delve into the introduction of prime numbers, exploring their definition, properties, and significance.
“Prime Numbers in Different Bases.” 2024. IX23. Accessed March 6, 2024. https://ix23.com/mathematics/integer-sequences/prime-numbers-in-different-bases/.
“Prime Numbers in Various Bases”. 2024. Prime Numbers in Various Bases. Wolfram Demonstrations Project. Accessed March 6, 2024. https://demonstrations.wolfram.com/PrimeNumbersInVariousBases/.
This Demonstration displays digit sequences of prime numbers up to a certain point in a specified base. Check “show digits” to overlay a numerical representation of each digit.
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Mathematical Mysteries 