Find the sum of the first 9 prime numbers.
The Correct Answer and Explanation is :
The correct answer is: 100
The first nine prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, and 23. To find their sum, we simply add these numbers together:
[
2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23
]
Calculating step by step:
- (2 + 3 = 5)
- (5 + 5 = 10)
- (10 + 7 = 17)
- (17 + 11 = 28)
- (28 + 13 = 41)
- (41 + 17 = 58)
- (58 + 19 = 77)
- (77 + 23 = 100)
Thus, the sum of the first nine prime numbers is 100.
Explanation
A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. This means that prime numbers cannot be formed by multiplying two smaller natural numbers. The smallest prime number is 2, which is also the only even prime number. All other prime numbers are odd.
The sequence of prime numbers starts with 2 and continues with 3, 5, 7, 11, and so on. Prime numbers play a crucial role in number theory and have applications in various fields, including cryptography, computer science, and mathematical proofs.
The first nine primes are particularly significant because they are foundational in the study of prime numbers. They serve as building blocks for understanding larger primes and the distribution of primes among natural numbers. The sum of these primes, which equals 100, provides a simple yet powerful example of their properties.
Understanding prime numbers helps us appreciate the structure and uniqueness of numbers. The concept of primes is not just limited to simple arithmetic; it extends to complex theories and applications in mathematics, such as the Fundamental Theorem of Arithmetic, which states that every integer greater than 1 can be uniquely factored into prime numbers. This property highlights the importance of primes in the mathematical landscape.