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

1. Apr 28, 2005

### tamalkuila

prove that primes of the form 4n+1 are infinite . send the proof at tamalkuila@gmail.com

Last edited by a moderator: May 11, 2014
2. Apr 28, 2005

### dfollett76

Hmmmm... Try doing a proof by contradiction.

3. Apr 28, 2005

### eNathan

Why would 4n+1 be infinite? n is an unknown variable. The only way the statment $$4n+1$$ is true is if $$n = infity$$.

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

Last edited: Apr 28, 2005
4. Apr 28, 2005

### HallsofIvy

Staff Emeritus
Good point, eNathan, but I think the original poster mean "the number of primes of the form 4n+1 is infinite".

5. Apr 28, 2005

### eNathan

Im a little confused with the logic of this question. What do prime numbers have to do with 4n+1?

6. Apr 28, 2005

### dfollett76

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