Prove that primes of the form 4n+1 are infinite

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Homework Help Overview

The discussion revolves around proving that there are infinitely many prime numbers of the form 4n+1. Participants are exploring the implications and reasoning behind this assertion within the context of number theory.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants suggest a proof by contradiction as a potential approach. Others question the meaning of the statement regarding 4n+1 and its relation to infinity, while one participant clarifies the definition of primes of the form 4n+1 with examples.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants are attempting to clarify the original poster's intent, while others are considering different methods of proof.

Contextual Notes

There appears to be some confusion regarding the relationship between prime numbers and the expression 4n+1, as well as the implications of the variable n in this context.

tamalkuila
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prove that primes of the form 4n+1 are infinite . send the proof at tamalkuila@gmail.com
 
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Hmmmm... Try doing a proof by contradiction.
 
Why would 4n+1 be infinite? n is an unknown variable. The only way the statement [tex]4n+1[/tex] is true is if [tex]n = infity[/tex].

PS >> Sorry I did not remember the \infity thing, it didnt work
 
Last edited:
Good point, eNathan, but I think the original poster mean "the number of primes of the form 4n+1 is infinite".
 
Im a little confused with the logic of this question. What do prime numbers have to do with 4n+1?
 
A prime of the the form 4n+1 is a prime that is equal to one more than four times an integer. In other words the prime when divided by four has a remainder of 1.

5, 13, 17, 29 are examples of primes of the form 4n+1.

5=4(1)+1
13=4(3)+1
17=4(4)+1
29=4(7)+1
 

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