ERROR 2013 (HY000) while importing large mysql dump file

[Adam S]

I'm trying to import these sql dump files. There are a bunch of them, all multiple gigs. Most are around 3-5gigs, one is 69gigs.

Well it gives me this error after a very short while:

ERROR 2013 (HY000) at line 103: Lost connection to MySQL server during query

The line number varies. Also, when it's processing, before it actually gives the error, if I try to login to phpMyAdmin to watch, it will sometimes let me login to the first page, but if I click anything it kicks me out.
And the sites that are running on the server that use the mysql server (different db) throw this db mysql error through the php:
Out of memory (Needed 536870880 bytes)

And then as soon as the error is throw:
Mysql reboots I think, the sites say they can't connect with provided settings. And if phpMyAdmin is sitting on the first page, it kicks me out.

So something is wrong...

what could it be?

help!! :(