Prime Numbers 400 to 500

A prime number is a natural number with no positive factors other than 1 and itself. Prime numbers can only be evenly divided by 1 and the number itself. Here are some properties of prime numbers: 

Every number greater than 1 is divisible by at least one prime number. 

Two different prime numbers are always relatively prime to each other. 

Every even positive integer greater than 2 can be expressed as the sum of two prime numbers. 

Every composite number can be uniquely factored into prime factors. 

Except for 2, all prime numbers are odd.

A prime number chart is a table showing prime numbers in increasing order within a specified range.

This chart helps in quickly identifying prime numbers between 400 and 500.

It is useful in mathematics and fields like cryptography and digital security.

Here is a list of all prime numbers between 400 and 500, providing a comprehensive view of numbers in this range that can only be divided by 1 and themselves.

All prime numbers, except for 2, are odd. This is because any even number greater than 2 can be divided by 2, making it non-prime. Thus, prime numbers between 400 and 500 are odd.

Prime numbers are natural numbers greater than 1 that can only be divided by 1 and themselves. Here are two methods to determine whether a number is prime: 

Divisibility Method:

To determine if a number is prime, check its divisibility by smaller prime numbers. If it is divisible by any of them, it is not prime. Example: Check if 439 is a prime number.

Step 1: 439 ÷ 2 = 219.5 (remainder ≠ 0)

Step 2: 439 ÷ 3 = 146.33 (remainder ≠ 0)

Step 3: 439 ÷ 5 = 87.8 (remainder ≠ 0)

Since 439 is not divisible by any of these, it is a prime number. 

Prime Factorization Method:

Break down composite numbers into the product of their prime factors. Example: Prime factorization of 450:

Step 1: 450 ÷ 2 = 225

Step 2: 225 ÷ 3 = 75

Step 3: 75 ÷ 3 = 25

Step 4: 25 ÷ 5 = 5

Step 5: 5 ÷ 5 = 1 (5 is prime)

Therefore, the prime factorization of 450 is 2 × 3² × 5².

Rule 1: Divisibility Check:

Prime numbers have no divisors other than 1 and themselves. Check for divisibility by numbers like 2, 3, 5, and 7. If divisible, the number is not prime.

Rule 2: Prime Factorization:

Break down numbers into their prime factors, showing them as products of prime numbers.

Rule 3: Sieve of Eratosthenes Method:

An ancient algorithm to find all prime numbers up to a given limit. List all numbers from 400 to 500. Start with the smallest prime, 2, and mark all multiples as non-prime.

Repeat with the next unmarked prime number, continuing until reaching the square root of 500 (approximately 22.36). The remaining unmarked numbers are prime.

•  Prime numbers: Natural numbers greater than 1, divisible only by 1 and themselves. Examples: 401, 409, 419, 421. 

• Odd numbers: Numbers not divisible by 2. All primes except 2 are odd. 

• Composite numbers: Non-prime numbers with more than 2 factors. Example: 450. 

• Prime factorization: Expressing a number as the product of its prime factors. Example: 450 = 2 × 3² × 5². 

• Sieve of Eratosthenes: An algorithm to find all prime numbers up to a limit by marking multiples of each prime.