Final answer:
The sum of the first 500 prime numbers cannot be easily computed without technical aids such as a computer program. Prime numbers are key elements in mathematics, starting with 2, 3, 5, 7, 11, etc., and the task to add them further up the series becomes increasingly complex.
Step-by-step explanation:
The question is asking for the sum of the first 500 prime numbers. Unlike the sum of the first five prime numbers which is given as 28, there isn’t a simple formula to calculate the sum of a large number of prime numbers such as 500. To find the sum of the first 500 prime numbers, one would typically use a computer program or algorithm to first generate all the prime numbers up to the 500th prime, and then add them all together. As this is a substantial task that cannot be easily performed here or done "in the head," the answer cannot be given without the use of such technology.
However, it's worth noting that prime numbers are a fundamental concept in number theory, and understanding their properties and distributions is a key part of mathematics. The list of prime numbers starts as 2, 3, 5, 7, 11, 13, 17, ..., and figuring out their sum as you go further along the series gets increasingly complex.
For students interested in computer science or advanced mathematics, writing a program to find primes and their sum could be a good exercise. It involves creating an efficient algorithm that can handle the computational load, especially as numbers get larger and the definition of prime numbers (numbers greater than 1 that have no positive divisors other than 1 and themselves) becomes harder to apply. Summing these primes to reach the total for the first 500 would be the final step of such a program.