Google's $3.14159bn bid for a raft of 6,000 patents from bankrupt Nortel Networks really was a mathematical joke - though the bidding was serious, as are the consequences

How much did Google bid for the collection of patents that Nortel Networks was selling off in its bankruptcy auction? At one point, $3.14159bn - which you don't have to be much of a maths whiz to realise is a billion dollars times pi, the fundamental mathematical number relating a circle's radius to its area and circumference.

And that wasn't all; at other points in the auction, in which Google was ranged against a six-strong consortium including Apple, Microsoft, BlackBerry maker RIM and Sony, the search engine company offered other amounts - $1,902,160,540 and $2,614,972,128 - which to mathematicians will jump out as Brun's constant (the number obtained by adding the reciprocals of the odd twin primes) and the Meissel-Mertens constant, another prime-related number.

To the people involved in the auction, though, the apparently random figures were puzzling. "Google was bidding with numbers that were not even numbers," one source involved with the auction told Reuters. "It [then] became clear that they were bidding with [numbers such as] the distance between the earth and the sun. One was the sum of a famous mathematical constant, and then when it got to $3 billion, they bid pi - $3.14159bn," the source said. "Either they were supremely confident or they were bored."

It is not the first time that Google has shown a liking for obscure mathematical jokes in its public acts: when it filed in 2004 to float on the US stock market, it sought to raise $2,718,281,828 - a multiple of e, the exponential constant. The company's founders Larry Page and Sergey Brin are both computer scientists, and the company is proud of the exceptional talents of its staff, who go through a rigorous interview process in which Page, the chief executive, still gets final approval.

Google lost the bid to a $4.5bn bid from the six-strong consortium. It had initially been expected to win the patents outright - which it was expected to use to shore up the competitive position of its Android mobile operating system against threats from Apple, Oracle and Nokia - when it made a $900m bid in April. But on Monday an auction began which saw 20 rounds of bidding between five consortia over four days. Google was finally outbid. Sources told Reuters that it had set a ceiling of around $4bn for the patents, despite having $36.7bn in cash at the end of its last financial quarter. Intel, its partner in the bid, had about $4bn in cash. But the opposing consortium had about $100bn in cash reserves.

Part of its tactic in choosing the mathematically-flavoured figures was that there would be almost no chance of being equal to a rival's bid - while also retaining the company's delight in showing off its prowess in handling figures.

But losing the patent bids may have serious longer-term effects. The patents relate to a number of communications protocols and methods which are increasingly useful, including so-called 4G communications, or "Long Term Evolution", and will therefore mean that their owners can extract licence fees from companies which want to use them. For Google, which faces a court challenge from database giant Oracle over its Android mobile operating system in which Oracle is seeking damages of $6.1bn, having the patents might have been a way to fight back - or at least bring in revenues from other companies in the mobile space.

"This is a sizable, strategically relevant portfolio," said Florian Mueller, an intellectual property analyst and blogger who has followed the progress of the bid through. "The bidding price presumably skyrocketed because bidders didn't just want to secure the patents for themselves: they also wanted to keep them out of the hands of at least some of the other bidders. There were two kinds of bidders: those who wanted to buy those patents as a strategic weapon and those whose mission was to clear the market and prevent these patents from being used in all the wrong ways. I guess the winning consortium made a defensive, market-clearing purchase."

But he said that missing out would hurt Google. "No major industry player is as needy in terms of patents as Google. There are already 45 patent infringement lawsuits surrounding Android and makers of Android-based devices have to pay royalties to dozens of right holders. Just this week Microsoft announced that three more Android device makers, in addition to HTC, are already paying royalties on Google's Android to Microsoft."

Mueller suggested that winning the auction could have solved all of Google's patent woes at once: "There are many entities asserting rights against Android whose calculus wouldn't have changed if Google had bought those patents. Oracle is a good example. Its lawsuit would have continued at any rate. But Google lost an unprecedented opportunity to acquire a major bargaining chip that would strengthen it at the mobile industry's intellectual property negotiating table. I'm afraid it won't get a similar opportunity in quantitative and qualitative terms anytime soon. It will have to continue to buy up smaller quantities of patents from failed startups and similar kinds of sellers. Those entities typically don't sell patents that read on a technology as essential as LTE [Long-Term Evolution communications standard].

"In light of Android's patent problems it's surprising that Google didn't outbid everyone else. It could have afforded more than $4.5 billion but it doesn't appear to be truly committed to Android."

It is not clear how ownership and licensing of the patents acquired by the winning consortium will be divided.

Five parties, including two consortiums, initially started bidding for 6,000 of the bankrupt Canadian telecoms company's patents - Apple, Intel, Google, a consortium of Ericsson, RIM, Microsoft, Sony and EMC, and a group led by patent risk solutions provider RPX, the sources told Reuters.

Intel started the bidding around 9 am on Monday with a $1.5 billion bid, one source said. The RPX-led consortium, which included Chinese firm Huawei, dropped out after the first round of the auction, held at the New York offices of law firm Cleary Gottlieb Steen & Hamilton LLP. The consortium remained on the sidelines looking to partner with someone else but never did.

"It did become clear to us very quickly that this was something that a bunch of big companies with humongous balance sheets had decided was strategic for them," RPX Chief Executive John Amster said. "Clearly at a price at this level it had to be strategic, and they could afford that."

The auction tested the limits of even the giants, and it took behind-the-scenes manoeuvring and a series of alignments for a winner to emerge. On Tuesday night, the Ericsson consortium stopped bidding, and started looking for a partner, which it found in Apple, the source said.

"When people drop out, you try to partner people," another source said. "It is pretty common in auctions because you are trying to get together people who have reached their individual limits and they still have interest in the assets." By Wednesday, Intel dropped out as well - a move that was followed by heated negotiations over the next 24 hours as the two remaining parties both tried to court the chip giant to join their side. Intel chose Google, one source said.

The field narrowed to two - the Apple consortium called "Rockstar," and the Google bidding vehicle named "Ranger", the sources told Reuters.

"Then it was fast and furious $100 million allotments until they got to $3 billion, at which point Google asked for permission to bid more," a source said. "They bid through $4 billion and tapped out."

Google declined to comment to Reuters, but called the auction results "disappointing."