# infinite primes?

• October 12th 2007, 01:28 PM
joanne_q
infinite primes?
hello guys . question here
how can i prove that there exists infinitely many primes p such that p = 3 mod 4.

i have a little inkling as i know that if a,b=1 mod 4 then ab = 1 mod 4. Im guessing it would be along the lines of euclids theorem?
• October 13th 2007, 12:05 AM
Opalg
Suppose there are only finitely many such primes, p_1, p_2, ..., p_n (where p_1=3). Look at the product $4p_2p_3\cdots p_n + 3$ and think about what its prime factors must look like.
• October 13th 2007, 04:42 PM
ThePerfectHacker
The case 4k+1 is more difficult.