# Nth term of prime number sequence

## Main Question or Discussion Point

I want somebody to help me what attempts have been made to understand the sequence of prime number. Is the Nth term of the sequence disclosed?

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I want somebody to help me what attempts have been made to understand the sequence of prime number. Is the Nth term of the sequence disclosed?
There is no explicit formula in N for the Nth prime if that is what you mean.

There is no explicit formula in N for the Nth prime if that is what you mean.

What attempts have been done to find nth term of prime numbers sequence?

What attempts have been done to find nth term of prime numbers sequence?
There are - on the other hand - algorithms (nor really formulas) to decide

- if a given number p is a prime
- if a given number q is composite (i.e. is not a prime)
- all primes between N0 and N1, if you know all prime numbers < Sqrt(N1)

There are - on the other hand - algorithms (nor really formulas) to decide

- if a given number p is a prime
- if a given number q is composite (i.e. is not a prime)
- all primes between N0 and N1, if you know all prime numbers < Sqrt(N1)

I know no specific web pages, but you can find details in a every textbook on basics of algorithmic number theory.
Best to start to write a computer algorithm as I did when I started computer
programing 45 years ago.
Key words for

problem (1): Fermats little theorem, quick exponentiation modulo N
problem (2): same as (1) + problem with Carmichael numbers
problem (3): expanded sieve of Eratosthenes

Regards, RamaWolf