The Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to a certain limit. It works by creating a list of numbers and then marking off the multiples of each prime number that is found, until the only numbers left are the primes. This algorithm is simple and efficient, but has some limitations in terms of the maximum size of numbers that it can handle.

The Riemann Hypothesis is a more advanced theory about the distribution of prime numbers. It states that the distribution of prime numbers is closely related to the distribution of a certain type of mathematical function called the Riemann zeta function. While this theory has not been proven, it has been the subject of much mathematical investigation and has important implications for many areas of mathematics and science.

For a 6 year old, you could explain the prime numbers as special numbers that can only be divided evenly by 1 and themselves. For example, the number 7 is a prime number because it can only be divided evenly by 1 and 7.
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