Prime Numbers | Examples, Types, Chart, Practice Questions

A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. In other words, a prime number can only be divided evenly by 1 and the number itself.

Examples of Prime Numbers

• The first 10 prime numbers are: 2,3,5,7,11,13,17,19,23,292, 3, 5, 7, 11, 13, 17, 19, 23, 29
• Notice that 2 is the only even prime number because every other even number is divisible by 2.

Types of Prime Numbers

1. Twin Primes: Two prime numbers that differ by 2.
   • Examples: (3,5),(11,13),(17,19)(3, 5), (11, 13), (17, 19)
2. Cousin Primes: Two prime numbers that differ by 4.
   • Examples: (7,11),(13,17)(7, 11), (13, 17)
3. Sexy Primes: Two prime numbers that differ by 6.
   • Examples: (5,11),(7,13)(5, 11), (7, 13)
4. Mersenne Primes: Prime numbers of the form 2n−12^n – 1, where nn is a positive integer.
   • Example: 31=25−131 = 2^5 – 1
5. Palindrome Primes: Prime numbers that are also palindromes (read the same forward and backward).
   • Examples: 101,131,151101, 131, 151

Prime Numbers Chart (1 to 100)

Here is a list of all prime numbers between 1 and 100:

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,972, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Properties of Prime Numbers

1. A prime number is greater than 1.
2. It has only two divisors: 1 and itself.
3. 2 is the smallest and the only even prime number.
4. All prime numbers greater than 2 are odd.
5. If a number has more than two divisors, it is called a composite number.

Practice Questions

1. Is 47 a prime number? Why or why not?
2. Identify the prime numbers between 50 and 70.
3. Prove whether 121 is a prime number.
4. Find the sum of all prime numbers between 1 and 20.
5. What is the 10th prime number?

Fun Fact

The largest known prime number (as of January 2025) is a Mersenne prime with over 24 million digits!

Understanding prime numbers is essential in fields like cryptography, computer algorithms, and number theory. Practice identifying and working with primes to build a strong mathematical foundation!