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“O.K.” was an exaggeration. Salander was better, but still in bad shape. For half of yesterday, in her apartment, she had been barely conscious and only managed with the greatest difficulty to drag herself out of bed to see that August had something to eat and drink and make sure he had pencils, crayons and paper. But as she approached him now she could see even from a distance that he had drawn nothing.

There was paper scattered all over the coffee table in front of him, but no drawings. Instead she saw rows of scribbles. More absent-mindedly than out of curiosity she tried to make out what they were — he had written numbers, endless series of numbers, and even if at first they made no sense to her, she was intrigued. Suddenly she gave a whistle.

“Oh my God,” she muttered.

They were staggeringly large numbers which formed a familiar pattern alongside the numbers next to them. As she looked through the papers and came across the simple sequence 641, 647, 653 and 659, there was no longer any doubt: they were sexy prime quadruplets, sexy in the sense that they differed from each other by six.

There were also twin primes, and every other imaginable combination of prime numbers. She could not help but smile. “Awesome.”

But August neither responded nor looked up at her. He just kept kneeling by the coffee table, as if he wanted nothing more than to go on writing his numbers. It occurred to her that she had read something about savants and prime numbers, but she put it out of her mind. She was far too unwell for any kind of advanced thinking. Instead she went into the bathroom and took two more Vibramycin antibiotics which had been lying around in her apartment for years.

She packed her pistol and her computer, a few changes of clothes and to be on the safe side she put on a wig and a pair of dark glasses. When she was ready she asked the boy to get up. He did not respond, just held his pencil in a tight grip. For a moment she stood in front of him, stumped. Then she said sternly, “Get up!” and he did.

They put on their outer layers, took the lift down to the garage and set off for the safe house on Ingarö. Her left shoulder was tightly strapped and it ached, so she steered with her right hand. The top of her chest was hurting, she had a fever and had to stop a couple of times at the side of the road to rest. When finally they got to the beach and the jetty by Stora Barnvik on Ingarö, and followed the directions to climb the wooden steps up the slope to the house, she collapsed exhausted on the first bed she saw. She was shivering and freezing cold.

Soon after, breathing laboriously, she got up and sat at the kitchen table with her laptop, and tried once more to crack the file she had downloaded from the N.S.A. But she did not even come close. August sat next to her, looking stiffly at the pile of paper and crayons Berger had left for him, no longer interested in prime numbers, still less in drawing pictures. Perhaps he was in shock.

The man who called himself Jan Holtser was sitting in a room at the Clarion Hotel Arlanda, talking on the telephone with his daughter. As he had expected, she did not believe him.

“Are you scared of me?” she said. “Are you afraid I’m going to cross-examine you?”

“No, Olga, absolutely not,” he said. “It’s just that...”

He could not find the words. He knew Olga could tell he was hiding something, and ended the conversation sooner than he wanted to. Bogdanov was sitting next to him on the hotel bed, swearing. He had been through Balder’s computer at least a hundred times and found “fuck all”, as he put it. “Not a single fucking thing!”

“I stole a computer with nothing on it,” Holtser said.

“Right.”

“So what was the professor using it for?”

“For something very important, clearly. I can see that a large file, presumably connected to other computers, was deleted recently. But I can’t recover it. He knew his stuff, that guy.”

“Useless,” Holtser said.

“Completely fucking useless.”

“And the Blackphone?”

“There are a couple of calls I haven’t been able to trace, presumably from the Swedish security services or the N.D.R.E. But there’s something bothering me much more.”

“What’s that?”

“A long conversation the professor had just before you stormed in — he was talking to someone at the M.I.R.I., Machine Intelligence Research Institute.”

“What’s the problem with that?”

“The timing — I get the feeling he was having some sort of crisis. Also this institute works to ensure that intelligent computers don’t become a threat to mankind — it doesn’t look good. Balder could have given the M.I.R.I. his research or...”

“Or what?”

“Or he could have spilled the beans on us, at least what he knew.”

“That would be bad.”

Bogdanov nodded and Holtser swore quietly. Nothing had gone as planned and neither of them was used to failing. But here were two major mistakes in a row, and all because of a child, a retarded child.

That was bad enough. But the worst of it was that Kira was on her way, and it sounded like she had lost it. Neither of them was used to that either. On the contrary, they had grown accustomed to her cool elegance, the air of invincibility it gave their operations. Now she was furious, completely off the wall, screaming at them that they were useless, incompetent cretins. It was not so much that those shots might have missed Balder’s son. It was because of the woman who had appeared out of nowhere and rescued the boy. That woman sent Kira around the bend.

When Holtser had begun to describe her — the little he had seen — Kira bombarded him with questions. Whatever answer he gave seemed to be wrong, or at least sent her berserk, yelling that they should have killed her and that this was typical of them, brainless, useless. Neither of them could make sense of her violent reaction — they had never heard her yell like that before.

In fact there was a lot they did not know about her. Holtser would never forget his evening with her in a suite at Hotel d’Angleterre in Copenhagen — they had had sex for the third or fourth time, and later they had been lying in bed drinking champagne and chatting about his wars and his murders, as they so often did. While stroking her arm he had discovered three scars side by side on her wrist.

“How did you get those, gorgeous?” he had said, and got a look of pure loathing in return.

He had never been allowed to sleep with her again. He took it to be a punishment for having asked. Kira looked after the group and gave them a lot of money. But neither he nor Bogdanov, nor anyone else in the group, was allowed to ask about her past. That was one of the unspoken rules and none of them would ever dream of trying. For better or for worse she was their benefactor, mostly for better, they thought, and they went along with her whims, living in constant uncertainty as to whether she would be affectionate or cold, or even give them a brutal, stinging slap.

Bogdanov closed the computer and took a swallow of his drink. They were trying to limit their drinking, so that Kira would not use that against them. But it was nearly impossible. The frustration and adrenalin drove them to it. Holtser fingered his mobile nervously.

“Didn’t Olga believe you?” Bogdanov said.

“Not a word. Soon she’ll see a child’s drawing of me on every billboard.”

“I don’t buy that drawing thing. Probably just wishful thinking on the part of the police.”

“So we’re supposed to kill a child for no reason?”

“It wouldn’t surprise me. Shouldn’t Kira be here by now?”

“Any time now.”

“Who do you think it was?”

“Who?”

“The girl who appeared from nowhere.”

“No idea,” Holtser said. “Not sure Kira knows either. But she’s worried about something.”