Nth term of prime number sequence

In summary, according to the article, there are algorithms to find the nth term of a sequence of prime numbers, but there is no explicit formula for calculating it.
  • #1
scimad
11
0
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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  • #2
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.
 
  • #3
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?
 
  • #5
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)
 
  • #6
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.
 
  • #7
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
 
  • #8

1. What is the formula for finding the Nth term of the prime number sequence?

The formula for finding the Nth term of the prime number sequence is N * (N - 1) + 2 . This formula works for all values of N greater than or equal to 1.

2. How do you use the formula to find the 10th term of the prime number sequence?

To find the 10th term of the prime number sequence, we plug in N = 10 into the formula: 10 * (10 - 1) + 2 = 92 . Therefore, the 10th term of the prime number sequence is 92.

3. Can the Nth term of the prime number sequence be a decimal or fraction?

No, the Nth term of the prime number sequence can only be a whole number. This is because prime numbers are only divisible by 1 and themselves, and therefore cannot be expressed as decimals or fractions.

4. What is the significance of the Nth term in the prime number sequence?

The Nth term in the prime number sequence represents the Nth prime number. This is useful in understanding and studying the patterns and properties of prime numbers.

5. Is there a limit to how large the Nth term of the prime number sequence can be?

There is no limit to how large the Nth term of the prime number sequence can be. As N increases, the Nth term will also increase, potentially becoming larger than any number we can imagine. This is because there is an infinite number of prime numbers.

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