What Defines the Nth Prime Number in Mathematics?

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The discussion centers on the concept of sequences in mathematics, specifically addressing the general term of a sequence. It establishes that a sequence can be represented as {an} where n is a natural number. The prime number sequence, {2, 3, 5, 7, ...}, is highlighted as lacking a straightforward formula, with the general term defined simply as "the nth prime." This definition suffices for mathematical purposes, as it uniquely identifies each prime number.

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  • Basic knowledge of prime numbers and their significance
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grupah
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Dear Forum,

Does every sequence have a general term? What is the definition of the general term of a sequence?

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hi grupah! :smile:

a sequence is a function whose domain is the natural numbers (or a subset of them)

so we can write it as {an}nεN,

and the general term of the sequence is an :wink:

(if you mean is there a straightforward formula for an, the answer is not necessarily, it depends how the sequence is defined)
 
What is your definition of sequence, exactly?
 
Is it possible to represent all the terms of the sequence by the general term?
 
i don't understand :confused:

can you give an example of what you're thinking of?​
 
Consider the sequence of prime numbers: {2,3,5,7,dots}
Does it have a general term?
 
grupah said:
Consider the sequence of prime numbers: {2,3,5,7,dots}
Does it have a general term?

no, there's no formula (other than "an is the nth prime")
 
So, what is the mathematical definition of the general term, a kind of explanation?
 
"the nth prime" is a mathematical definition!

it uniquely defines the number, and that's all maths requires :smile:
 

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