103 LearnersLast updated on July 1st, 2025
Prime Numbers 1 to 100000
The natural numbers greater than 1 are called prime numbers. Prime numbers have only two factors, 1 and the number itself. Besides math, we use prime numbers in many fields, such as securing digital data, radio frequency identification, etc. In this topic, we will learn about the prime numbers 1 to 100000.
Prime Numbers 1 to 100000
A prime number is a natural number with no positive factors other than 1 and the number itself. And the prime number can only be evenly divisible by 1 and the number itself. Here are some basic properties of prime numbers:
- Every number greater than 1 is divisible by at least one prime number.
- Two prime numbers are always relatively prime to each other.
- Every even positive integer greater than 2 can be written as the sum of two prime numbers (Goldbach's conjecture).
- Every composite number can be uniquely factored into prime factors.
- Except for 2, all prime numbers are odd; 2 is the only even prime number.
Prime Numbers 1 to 100000 Chart
A prime number chart is a table showing the prime numbers in increasing order. The chart simply includes all the prime numbers up to a certain limit for identifying the prime numbers within a range.
For kids, it will be less difficult to understand the prime numbers through the chart. The significance of this prime number chart is used in different fields like the foundation of mathematics and the fundamental theorem of arithmetic.
List of All Prime Numbers 1 to 100000
The list of all prime numbers from 1 to 100000 provides a comprehensive view of numbers in this range that can only be divided by 1 and the number itself.
Prime Numbers - Odd Numbers
Prime numbers and odd numbers are the numbers that are only divisible by 1 and the number itself. They cannot be evenly divisible by 2 or other numbers. 2 is the only even prime number, which divides all the non-prime numbers. Therefore, except for 2, all prime numbers are considered as the set of odd numbers.
How to Identify Prime Numbers 1 to 100000
Prime numbers are a set of natural numbers that can only be divided by 1 and the number itself. Here are the two important ways to find whether a number is prime or not.
By Divisibility Method:
To find whether a number is prime or not, we use the divisibility method to check. If a number is divisible by 2, 3, or 5 then it will result in a non-prime number. Prime numbers are only divisible by 1 and itself, so if a number is divisible by the number itself and 1, it is a prime number.
For example: To check whether 101 is a prime number,
Step 1: 101 ÷ 2 = 50.5 (not divisible)
Step 2: 101 ÷ 3 = 33.67 (not divisible)
Step 3: 101 ÷ 5 = 20.2 (not divisible)
Since no divisors are found, 101 is a prime number.
By Prime Factorization Method:
The prime factorization method is the process of breaking down a composite number into the product of its prime factors. The method of prime factorization helps to identify the prime numbers up to 100000 by building the smallest blocks of any given number.
For example: The prime factorization of 100000: Let's break it down into the smallest prime numbers until it can’t divide anymore.
Step 1: 100000 ÷ 2 = 50000
Step 2: 50000 ÷ 2 = 25000
Step 3: 25000 ÷ 2 = 12500
Step 4: 12500 ÷ 2 = 6250
Step 5: 6250 ÷ 2 = 3125
Step 6: 3125 ÷ 5 = 625
Step 7: 625 ÷ 5 = 125
Step 8: 125 ÷ 5 = 25
Step 9: 25 ÷ 5 = 5
Step 10: 5 ÷ 5 = 1
Therefore, the prime factorization of 100000 is: 100000 = 25 × 55.
Rules for Identifying Prime Numbers 1 to 100000
Rule 1: Divisibility Check: Prime numbers are natural numbers that are greater than 1 and have no divisors other than 1 and the number itself. In the divisibility check rule, we check whether the prime number is divisible by 2, 3, 5, 7, 11, 13, etc. If it's divisible by these numbers then it's not a prime number.
Rule 2: Prime Factorization: In this prime factorization method, we break down all the numbers into their prime factors, showing them as the product of prime numbers.
Rule 3: Sieve of Eratosthenes Method: The method, Sieve of Eratosthenes, is an ancient algorithm used to find all prime numbers up to a given limit. First, we list all the numbers from 1 to 100000. Then start with the first prime number, 2. Mark all the multiples of 2 as non-prime.
Repeat the process for the next unmarked prime number and continue until you reach the square root of 100000, approximately 316. The remaining unmarked numbers are the prime numbers.
Tips and Tricks for Prime Numbers 1 to 100000
- Use common shortcuts to memorize the prime numbers. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, use these numbers as references.
- Practice using the method of Sieve of Eratosthenes efficiently. Numbers like 4, 8, 9, 16, 25, 36 are never meant to be prime.
- Knowing the common powers of numbers helps in avoiding unnecessary checks.
Common Mistakes and How to Avoid Them in Prime Numbers 1 to 100000
While working with the prime numbers 1 to 100000, children might encounter some errors or difficulties. We have many solutions to resolve those problems. Here are some given below:
Mistake 1
Confusing composite numbers with prime numbers.
A prime number has exactly 2 divisors: 1 and the number itself. Remember that composite numbers have more than 2 divisors. For example, 9 is not a prime number because it has more than 2 divisors.
Mistake 2
Including 1 as a prime number.
Always remember that primes are greater than 1. 1 is not a prime number because it has only one divisor, itself.
Mistake 3
Not efficiently using the prime checking method.
Practice using the method of Sieve of Eratosthenes efficiently, or check divisibility by primes up to the square root of the number. For example, while checking the divisibility of 289, stop once you reach √289.
Mistake 4
Not realizing about the primes in the larger prime range.
Keep on practicing identifying the larger primes, as it helps to sharpen the skills of children. The usage of the method of Sieve of Eratosthenes helps to solve this.
Mistake 5
Forgetting that multiples of any prime number are not prime.
Erase all the multiples of known prime numbers as soon as possible. For example, if you're checking numbers up to 100000, you don't have to check numbers divisible by 2, 3, 5, or 7 because they are not prime.
Prime Numbers Examples
Problem 1
Is 99991 a prime number?
Yes, 99991 is a prime number.
Explanation
To determine if 99991 is a prime number, check divisibility by primes up to √99991, approximately 316. (2, 3, 5, 7, 11, ..., 311).
99991 ÷ 2 = 49995.5
99991 ÷ 3 = 33330.33
99991 ÷ 5 = 19998.2
99991 ÷ 7 = 14284.4285
99991 ÷ 11 = 9081.9091
Since 99991 is not divisible by any of these numbers, 99991 is a prime number.
Problem 2
Jenna wants to send a secret message using the largest prime number under 100000. Which prime number should she use?
99991 is the largest prime number under 100000, and Jenna should use it for her secret message.
Explanation
Prime numbers are natural numbers greater than 1 with no divisors other than 1 and the number itself. Under 100000, the largest prime number is 99991, making it ideal for secure communication.
Problem 3
A mathematician asks: What is the largest prime number less than 1000 that is closest to 1000?
997 is the largest prime number less than 1000.
Explanation
997 is a prime number because it is only divisible by 1 and the number itself. The next prime number, 1009, is greater than 1000. Therefore, the largest prime number less than 1000 is 997.
FAQs on Prime Numbers 1 to 100000
1.Give some examples of prime numbers.
2.Explain prime numbers in math.
3.Is 2 the smallest prime number?
4.Which is the largest prime number?
5.Which is the largest prime number in 1 to 100000?
6.How can children in Saudi Arabia use numbers in everyday life to understand Prime Numbers 1 to 100000?
7.What are some fun ways kids in Saudi Arabia can practice Prime Numbers 1 to 100000 with numbers?
8.What role do numbers and Prime Numbers 1 to 100000 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Prime Numbers 1 to 100000 skills?
Important Glossaries for Prime Numbers 1 to 100000
- Prime numbers: The natural numbers which are greater than 1 and that are divisible by 1 and the number itself. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and so on.
- Odd numbers: The numbers that are not divisible by 2 are called odd numbers. All prime numbers except 2 are odd. For example, 3, 5, 7, 9, 11, 13, and so on.
- Composite numbers: Composite numbers are non-prime numbers that have more than 2 factors. For example, 12 is a composite number, and it is divisible by 1, 2, 3, 4, 6, and 12.
- Divisibility: A method used to determine if one number is a factor of another. For example, a number divisible by 2 is even.
- Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a given limit by iteratively marking the multiples of each prime starting from 2.
Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
