# How many prime numbers have we actually solved

• evolvehuman
In summary, the conversation revolved around the topic of prime numbers and their infinite nature. The usual way of proving the infinitude of prime numbers was mentioned, as well as the idea of using Fermat numbers to find new primes. However, the conversation also touched on the possibility of there being gaps in the sequence of prime numbers and the difficulty of finding a formula for all prime numbers. The conversation ended with a request to prove a specific number to be prime using the Euclid-Mullin sequence, but this was deemed as a ridiculous request and the thread was closed.
evolvehuman
how many prime numbers have we actually solved,,, how can we say that there is no end to prime when we can't even count that high, i think sooner or later all numbers higher than primegod would be not prime

evolvehuman said:
how can we say that there is no end to prime when we can't even count that high, i think sooner or later all numbers higher than primegod would be not prime

The usual way of proing that there are infinitely many primes is Euclid's proof: if the only primes were (p1, p2, ..., pk) then P = p1 * p2 * ... * pk + 1 cannot be divisible by any of p1, ..., pk, and so P is divisible by a prime other than p1, ..., pk.

One technique you might like: the Fermat numbers 2^(2^n) + 1 are pairwise relatively prime, so each contains at least one prime not previously occurring as a Fermat number divisor.

i still believe the math is going to egg

evolvehuman said:
i still believe the math is going to egg

Hmm... I don't think so. At least I'm not going to hold my breath.

further prime should have a different formula or all prime won't be contained

unless we are just trying to find any prime then there will be holes in the grid

evolvehuman said:
further prime should have a different formula or all prime won't be contained

Do you mean that the Euclid-Mullin sequence, Sloane's A000945, doesn't contain all primes?

That problem is still open. If you think you have a proof, try to write it up.

just being dumb prove 139 is prime by the e-m sequence for me please, ...
a(1) = 2, a(n+1) _{k=1..n} a(k) + 1

This is ridiculous. I am closing the thread.

## 1. How do we define a prime number?

A prime number is a positive integer that is only divisible by 1 and itself. In other words, it has no other factors besides 1 and itself.

## 2. What is the largest known prime number?

As of 2021, the largest known prime number is 2^82,589,933 - 1, which is a number with 24,862,048 digits. It was discovered in December 2018 by the Great Internet Mersenne Prime Search (GIMPS) project.

## 3. How many prime numbers have been discovered so far?

There are infinitely many prime numbers, so it is impossible to determine an exact number. However, as of 2021, the largest known prime number is 2^82,589,933 - 1, and there are over 51 million known prime numbers with at least 100 million digits.

## 4. How do we find new prime numbers?

There are various methods for finding prime numbers, such as the Sieve of Eratosthenes and the Sieve of Atkin. These methods involve systematically checking for numbers that are only divisible by 1 and themselves. There are also advanced algorithms and computer programs used to find larger and more complex prime numbers.

## 5. Is there a pattern to the distribution of prime numbers?

There is no known pattern to the distribution of prime numbers. They appear to occur randomly, with no discernible pattern or formula. This is known as the "mystery of prime numbers" and it continues to baffle mathematicians and scientists.

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