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.
tamalkuila
Messages
4
Reaction score
0
prove that primes of the form 4n+1 are infinite . send the proof at tamalkuila@gmail.com
 
Last edited by a moderator:
Physics news on Phys.org
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
 
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
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Prove that there are infinitely many primes of the form ## 8k-1 ##
Replies
4
Views
2K
I Infinitely many primes of the form p² + nq² -- really?
Replies
8
Views
2K
Prove that there are infinitely many primes of the form ## 6k+1 ##?
Replies
12
Views
3K
Are Primes of the Form 4n+1 Infinite?
Replies
10
Views
6K
A How should I write an account of prime numbers?
Replies
5
Views
2K
The only prime of the form n^3-1 is 7?
Replies
2
Views
4K
The only prime of the form n^2-4 is 5?
Replies
2
Views
3K
Prove that there exists a prime with at least ## n ## of its digits.
Replies
2
Views
2K
Show that the primes of the form 4n-1 and 4n +1 are infinite
Replies
2
Views
12K
MHB Are There Infinite Primes of the Form 4k + 1?
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top