Last updated on July 1st, 2025
Prime numbers are natural numbers greater than 1 with only two factors: 1 and the number itself. They play a crucial role in various fields, such as cryptography, digital security, and more. In this topic, we will explore prime numbers from 1 to 1,000,000.
A prime number is a natural number that has no positive divisors other than 1 and itself. Here are some key properties of prime numbers:
A prime number chart displays prime numbers in increasing order, helping to identify primes within a specified range. Such charts are useful for understanding the distribution of prime numbers and are applied in fields like cryptography and number theory.
The list of all prime numbers from 1 to 1,000,000 provides an extensive view of numbers in this range that can only be divided by 1 and the number itself. The prime numbers in this range include:
Prime numbers and odd numbers share the property of having no divisors other than 1 and themselves. All prime numbers except for 2 are odd, making the set of prime numbers a subset of odd numbers.
Prime numbers can be identified using a couple of methods:
Check divisibility by known small primes (e.g., 2, 3, 5, 7) to determine if a number is prime.
For example, to verify if 29 is prime: -
29 ÷ 2 = 14.5 (not divisible)
29 ÷ 3 = 9.66 (not divisible)
29 ÷ 5 = 5.8 (not divisible)
Since no divisors are found, 29 is a prime number.
Break down composite numbers into their prime factors. For example, the prime factorization of 100: -
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
Thus, the prime factorization of 100 is: 100 = 2² × 5².
Rule 1: Divisibility Check: Prime numbers have no divisors other than 1 and themselves. Check divisibility by small primes. If divisible, the number is not prime.
Rule 2: Prime Factorization: Break down numbers into their prime factors to identify non-prime numbers. Rule 3: Sieve of Eratosthenes Method: List numbers up to 1,000,000, starting with 2. Mark multiples of each prime as non-prime. Continue with the next unmarked number. Unmarked numbers are prime.
While working with prime numbers, people might encounter errors. Here are some solutions:
Is 104729 a prime number?
Yes, 104729 is a prime number.
The square root of 104729 is approximately 323.7. Check divisibility by primes less than 323.7. (2, 3, 5, 7, 11, ..., 317).
104729 ÷ 2 = 52364.5
104729 ÷ 3 = 34909.67
104729 ÷ 5 = 20945.8
104729 ÷ 7 = 14961.29
104729 ÷ 11 = 9511.73
Since 104729 is not divisible by any of these numbers, it is a prime number.
Alex is trying to open a digital locker with a 6-digit number. The code is the largest prime number under 1,000,000. Which prime number will open the lock?
The largest prime number under 1,000,000 is 999983.
Prime numbers are natural numbers greater than 1 with no divisors other than 1 and themselves. In the range up to 1,000,000, 999983 is the largest prime number, hence it is the code for the digital locker.
A teacher challenges her students: Find the prime numbers that are closest to 100 but less than 100.
97 is the prime number closest to 100.
97 is a prime number because it is only divisible by 1 and itself. The next prime number is 101, which is greater than 100. Therefore, the prime number closest to but less than 100 is 97.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.