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Applied Mathematics · Ch 1 — Numbers and Quantification

Prime Numbers

1.2

Prime Numbers

Prime numbers are the fundamental building blocks of all natural numbers — every integer greater than 1 can be broken down into a unique product of primes. Understanding them is not just about memorising a list; it is about seeing the elegant structure that underpins arithmetic itself. In this section, we will explore what makes a number prime, how to test for primality, and why these indivisible numbers matter so much in mathematics and its applications.

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Figure 1.1aThe Sieve of Eratosthenes, step 1: starting from a grid of 1 to 100, the number 2 is kept as prime and every larger multiple of 2 is struck out
Fig. 1.1a — The Sieve of Eratosthenes, step 1: starting from a grid of 1 to 100, the number 2 is kept as prime and every larger multiple of 2 is struck out

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

Step 1 of the sieve: keep 2, then strike out every larger mul …

Figure 1.1bThe Sieve of Eratosthenes, step 2: after also striking the multiples of 3 and 5, the numbers left uncrossed are the prime numbers up to 100
Fig. 1.1b — The Sieve of Eratosthenes, step 2: after also striking the multiples of 3 and 5, the numbers left uncrossed are the prime numbers up to 100

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

Step 2: after striking the multiples of 2, 3 and 5, the numbers left uncrossed …

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