Nth term of prime number sequence

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Discussion Overview

The discussion revolves around the attempts to understand the sequence of prime numbers, specifically regarding the existence of an explicit formula for the Nth term of the prime number sequence. Participants explore various algorithms related to prime identification and the challenges in formulating a direct expression for the Nth prime.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants express uncertainty about whether an explicit formula exists for the Nth prime number.
  • Algorithms exist to determine if a number is prime or composite, as well as to list all primes within a certain range, but these are not considered formulas for the Nth prime.
  • One participant suggests that textbooks on algorithmic number theory contain relevant information, and mentions specific problems related to prime identification.
  • Links to external resources and algorithms are requested by participants, indicating a desire for further exploration of the topic.

Areas of Agreement / Disagreement

Participants generally agree that there is no explicit formula for the Nth prime, but multiple views remain regarding the effectiveness and nature of algorithms used to identify primes.

Contextual Notes

Some participants mention specific problems and algorithms without providing detailed explanations, leaving certain assumptions and definitions unresolved.

Who May Find This Useful

This discussion may be useful for individuals interested in number theory, algorithm development, and the study of prime numbers.

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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