FTA: While it took years for the original Human Genome Project to analyze a single human genome (some 3 billion DNA base pairs), modern lab equipment with microfluidic chips can do it in hours.

OK, so assuming 1 hour for 3 billion bases, it's 1000 hours for 3 trillions bases (3 Terabits) or 1 million hours for ~3 petabits (or 400TBs of data). Yeah, that's a long time, roughly 100 years :)

Reading DNA is advancing fairly quickly. Illumina's HiSeq X Ten system produces 6Tbases per day. (Capex and opex/year are both in the 8 digit range.)

Seeking can be performed through entirely different means, as DNA is content-addressable. You can put in a magnetic bead attached to a strand complementary to what you're seeking, and pull that out of the mix. This is still a physical process that can take quite a bit of time.

Read and write were a couple of days each. Would be faster now. That said, we did 650kB; the article is misleading as they are talking about copies of the same information.