You will need to do intermediate upgrades. The jump from 3.x to 4.x is a big one and that's the one that you have to step up to if you want to go to 5.x/6.x first.
I'd go 3.13 to 4.4.latest, and I think I'd probably go to 5.2 or 6.0 before 7 as well.
As of JIRA 5 we dropped upgrade tasks for versions less than 4.0, so as everyone else says you have to go to 4.4.5 first. No need to go through the other major versions, all the upgrade tasks are still in the later versions. 3.13 > 4.4.5 > 7.0
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