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

AI Thread Summary
Primes of the form 4n+1 are defined as primes that yield a remainder of 1 when divided by 4. The discussion centers on proving that there are infinitely many such primes, with suggestions to use proof by contradiction. Participants express confusion about the logic behind the question and clarify the definition of primes in this context. Examples of primes fitting this form include 5, 13, 17, and 29, demonstrating the concept. The conversation highlights the need for a rigorous proof to establish the infinitude of these primes.
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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 4n+1 is true is if n = infity.

PS >> Sorry I did not remember the \infity thing, it didnt work
 
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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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