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What are the 25 prime numbers between 1 and 100?

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The first 25 prime numbers are two, three, five, seven, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. A prime number is a positive value only divisible by itself and the number one. For instance, the number 11 has two factors: one and 11.

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Greek mathematicians studied prime numbers as far back as 300 BCE when Euclid published a series of theorems in his treatise "Elements." Euclid's work demonstrated that all non-prime numbers, or composites, are made up of a unique combination of prime numbers. In other words, a series of prime numbers can be multiplied to produce each composite number. For example, 2 x 3 = 6, and 2 x 2 x 3 = 12.

Mathematician Eratosthenes designed a rudimentary algorithm in 200 BCE that used a grid system to quickly sort out divisible numbers. The series of prime numbers is considered infinite, and as of May 2013, the largest one discovered contained 17,425,170 digits.

In modern society, prime numbers are used for security encryption, especially in banking and Internet commerce. Large composite numbers are difficult to break down to individual factors, creating a time-consuming roadblock for codebreakers.

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Related Questions

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The list of prime numbers continues infinitely, as stated by Euclid’s theorem. The prime numbers less than 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. A number is regarded as prime if it can only be divided by 1 and itself.

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Prime numbers are important in mathematics because they function as indivisible units and serve as the foundation of several mathematical disciplines. Because a prime number is a natural number greater than 1 that can only be divided by itself and 1, all non-prime numbers, which are called composite numbers, can be factored into a unique set of prime numbers. Computer security programs and cryptology are two fields that have made use of prime numbers to code and decode sensitive information.

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To find prime numbers, use factorization to break down numbers and test whether they are prime or not. Numbers that are prime only have themselves and 1 as their factors; if they break down into other smaller numbers, they are not prime.