The Google boys wanted to show off their number theory chops. Steve Jobs needed to win.

Google's Page and Brin

Perhaps if it had been Google GOOG that was getting hauled into court for patent violations it would have fought harder to win this week’s auction for the rich portfolio of intellectual property bequeathed by the bankrupt Nortel Corp.

But it was Google’s Android partners — the HTCs, Motorolas and Samsungs of the world — that were getting sued for making smartphones that look and feel suspiciously like the iPhone.

And when bidding for the patents that would have bought Android some legal protection got serious, Google started playing games.

Quoting “three people with direct knowledge of the situation,” Reuters reported late Friday that Google was making bids that were literally irrational — using numbers like Brun’s constant (1.902160540…), the Meissel-Mertens constant (0.2614972128…) and, when they got permission to go past the $3 billion limit, pi (3.14159…).

“Google was bidding with numbers that were not even numbers,” one of Reuters’ sources said.

That may have impressed the math majors at Stanford, but it had no effect on the deadly serious businessmen they were bidding against. Apple AAPL , having just settled a 20-month legal battle with Nokia NOK and facing a potential import ban in its epic struggle with Samsung, was particularly determined. In the end it was they who led the consortium that shelled out $4.5 billion for Nortel’s 6,000 patents — the largest sum, by far, ever paid for a collection of intellectual properties.

According to Mark Stephens, who writes under the byline Robert X. Cringely, the cost — and the spoils — were split as follows:

  • Apple paid $2 billion “for outright ownership of Nortel’s Long Term Evolution (4G) patents as well as another package of patents supposedly intended to hobble Android.”
  • Research in Motion RIMM and Ericsson ERIC together put up $1.1 billion “with Ericsson getting a fully paid-up license to the portfolio, while RIM… gets a paid-up license plus possibly some carry forward operating losses from Nortel” for a break in its Canadian taxes.
  • Microsoft MSFT and Sony SNE put up another $1 billion.
  • EMC EMC reportedly paid $400 million in a side deal for a subset of patents related to its storage business.

Larry Page and Sergey Brin got the pleasure of proving that they still remember their number theory.