The Sum of Prime Numbers Between 1 and 25: A Detailed Guide

Prime numbers are a fundamental concept in number theory, and understanding them deepens our appreciation for the structure of integers. This guide will explore the sum of all prime numbers between 1 and 25. We will start by identifying these prime numbers, then calculate their sum both manually and through a programming algorithm. Finally, we will conclude with a summary of our findings.

Identifying Prime Numbers

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Intuitively, this means a prime number cannot be divided evenly by any other number except 1 and itself.

Prime Numbers Between 1 and 25

2 3 5 7 11 13 17 19 23

Note that the number 1 is not considered a prime number. This is a well-established mathematical convention, and every authoritative source agrees on this point.

Summing the Prime Numbers

Manual Calculation

To find the sum of the prime numbers between 1 and 25, we need to add them up:

2 3 5 7 11 13 17 19 23

Breaking it down 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 all the prime numbers between 1 and 25 is 100.

Using Programming Algorithm

While the manual approach is informative, programming can make it much more efficient, especially for larger ranges. Here is a simple algorithm to achieve this:

Take numbers between 1 and 25. Loop through each number to count its factors. Store numbers that have exactly two factors (1 and itself) in a variable.

for number in range(1, 26):
    factors  0
    for i in range(1, number   1):
        if number % i  0:
            factors   1
    if factors  2:
        add   number

The variable add will hold the sum of all prime numbers between 1 and 25.

Conclusion

In conclusion, the sum of all prime numbers between 1 and 25 is 100. Understanding prime numbers and their properties is crucial in many areas of mathematics and computer science. Whether you're calculating manually or using a program, the sum remains consistent with the manually calculated result.

If you have any further questions or need more examples, feel free to explore more about prime numbers and their sums!