Nth term of prime number sequence

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There is no explicit formula for determining the Nth prime number in the sequence, although various algorithms exist to identify prime and composite numbers. These algorithms can determine if a number is prime, identify composite numbers, and list all primes within a specified range if the primes below the square root of the upper limit are known. Resources for understanding these algorithms can typically be found in textbooks on algorithmic number theory. Users are encouraged to explore links and references related to prime number algorithms for deeper insights. The quest for a definitive Nth term formula remains an open question in mathematics.
scimad
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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?
 
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scimad said:
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.
 
ramsey2879 said:
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?
 
scimad said:
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)
 
RamaWolf said:
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)

Please help me to know to the links to the algorithms to the pages where they are discussed.
 
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
 

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