Sending email with postfix doesn't reach recipient

I'm trying to troubleshoot a problem with my postfix server not sending email to my GMail account (as a test).

From /var/log/mail.log:

Jan  6 07:46:37 todo postfix/smtp[5818]: connect to alt1.gmail-smtp-in.l.google.com[64.233.186.27]:25: Connection timed out
Jan  6 07:46:37 todo postfix/smtp[5818]: connect to alt2.gmail-smtp-in.l.google.com[2a00:1450:400b:c00::1b]:25: Network is unreachable
Jan  6 07:46:37 todo postfix/smtp[5818]: 334FF1391C9: to=<[email protected]>, relay=none, delay=1443, delays=1383/0.01/60/0, dsn=4.4.1, status=deferred (connect to alt2.gmail-smtp-in.l.google.com[2a00:1450:400b:c00::1b]:25: Network is unreachable)

I don't want to relay via gmail, but the receiving email is at a gmail address. Is postfix trying to use gmail as a relay somehow?

In /etc/postfix/main.cf I have:

relay_host = 

Solution 1:

From another answer on StackOverflow: it looks like Amazon blocks outbound traffic on port 25, and a request has to be submitted to have this block removed:

https://aws.amazon.com/premiumsupport/knowledge-center/ec2-port-25-throttle/?nc1=h_ls

Thanks to Gerald for pointing out it was a firewall issue!