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August stared at the table as he continued rocking and did not look as if he understood anything at all.

“Prime-number factorization is when we rewrite a number as the product of prime numbers. By product in this context I mean the result of a multiplication. Do you follow me?”

August’s expression did not change, and Salander wondered if she should just shut up.

“According to the fundamental principles of arithmetic, every whole number has a unique prime-number factorization. It’s pretty cool. We can produce a number as simple as 24 in all sorts of ways, for example by multiplying 12 by 2 or 3 by 8, or 4 by 6. Yet there’s only one way to factorize it with prime-numbers and that’s 2 x 2 x 2 x 3. Are you with me? The problem is, even though it’s easy to multiply prime numbers to produce large numbers, it’s often impossible to go the other way, from the answer back to the prime numbers. A really bad person has used this to code a secret message. Do you understand? It’s a bit like mixing a drink: easy to do but harder to unmix again.”

August neither nodded nor said a word. But at least his body was no longer rocking.

“Shall we see if you’re any good at prime-number factorization, August? Shall we?”

August did not budge.

“I’ll take that as a yes. Shall we start with the number 456?”

August’s eyes were bright but distant, and Salander had the feeling that this idea of hers really was absurd.

It was cold and windy and there were few people out. But Blomkvist thought the cold was doing him good — he was perking up a bit. He thought of his daughter Pernilla and what she said about writing “for real”, and of Salander of course, and the boy. What were they doing right now?

On the way up towards Hornsgatspuckeln he stared for a while at a painting hanging in a gallery window which showed cheerful, carefree people at a cocktail party. At that moment it felt, perhaps wrongly, as if it had been ages since he had last stood like that, drink in hand and without a care in the world. Briefly he longed to be somewhere far away. Then he shivered, suddenly struck by the feeling that he was being followed. Perhaps it was a consequence of everything he had been through in the last few days. He turned round, but the only person near him was an enchantingly beautiful woman in a bright red coat with flowing dark blonde hair. She smiled at him a little uncertainly. He gave her a tentative smile back and was about to continue on his way. Yet his gaze lingered, as if he were expecting the woman to turn at any moment into something more run-of-the-mill.

Instead she became more dazzling with each passing second, almost like royalty, a star who had accidentally wandered in among ordinary people, a gorgeous spread in a fashion magazine. The fact was that right then, in that first moment of astonishment, Blomkvist would not have been able to describe her, or provide even one single detail about her appearance.

“Can I help you?” he said.

“No, no,” she said, apparently shy, and there was no getting away from it: her hesitancy was beguiling. She was not a woman you would have thought to be shy. She looked as if she might own the world.

“Well then, have a nice evening,” he said, and turned again, but he heard her nervously clear her throat.

“Aren’t you Mikael Blomkvist?” she said, even more uncertain now, looking down at the cobbles in the street.

“Yes, I am,” he said, and smiled politely, as he would have done for anybody.

“Well, I just want to say that I’ve always admired you,” she said, raising her head and gazing into his eyes with a long look.

“I’m flattered. But it’s been a long time since I wrote anything decent. Who are you?”

“My name is Rebecka Mattson,” she said. “I’ve been living in Switzerland.”

“And now you’re home for a visit?”

“Only for a short time, unfortunately. I miss Sweden. I even miss November in Stockholm. But I guess that’s how it is when you’re homesick, isn’t it?”

“What do you mean?”

“That you miss even the bad bits.”

“True.”

“Do you know how I cure it all? I follow the Swedish press. I don’t think I’ve missed a single issue of Millennium in the last few years,” she said. He looked at her again, and noticed that every piece of clothing, from the black high-heeled shoes to the checked blue cashmere shawl, was expensive and elegant.

Rebecka Mattson did not look like your typical Millennium reader. But there was no reason to be prejudiced, even against rich expatriate Swedes.

“Do you work there?” he said.

“I’m a widow.”

“I see.”

“Sometimes I get so bored. Were you going somewhere?”

“I was thinking of having a drink and a bite to eat,” he said, at once regretting his reply. It was too inviting, too predictable. But it was at least true.

“May I keep you company?” she asked.

“That would be nice,” he said, sounding unsure. Then she touched his hand — unintentionally, at least that is what he wanted to believe. She still seemed bashful. They walked slowly up Hornsgatspuckeln, past a row of galleries.

“How nice to be strolling here with you,” she said.

“It’s a bit unexpected.”

“So true. It’s not what I was thinking when I woke up this morning.”

“What were you thinking?”

“That the day would be as dreary as ever.”

“I don’t know if I’ll be such good company,” he said. “I’m pretty much immersed in a story.”

“Are you working too hard?”

“Maybe so.”

“Then you need a little break,” she said, giving him a bewitching smile, filled with longing or some sort of promise. At that moment he thought she seemed familiar, as if he had seen that smile before, but in another form, distorted somehow.

“Have we met before?” he said.

“I don’t think so. Except that I’ve seen you a thousand times in pictures, and on T.V.”

“So you’ve never lived in Stockholm?”

“When I was a little girl.”

“Where did you live then?”

She pointed vaguely up Hornsgatan.

“Those were good times,” she said. “Our father took care of us. I often think about him. I miss him.”

“Is he no longer alive?”

“He died much too young.”

“I’m sorry.”

“Thank you. Where are we headed?”

“Well,” he said, “there’s a pub just up Bellmansgatan, the Bishops Arms. I know the owner. It’s quite a nice place.”

“I’m sure...”

Once again she had that diffident, shy look on her face, and once again her hand happened to brush against his fingers — this time he wasn’t so sure it was accidental.

“Perhaps it isn’t fancy enough?”

“Oh, I’m sure it’s fine,” she said apologetically. “It’s just that people tend to stare at me. I’ve come across so many bastards in pubs.”

“I can believe that.”

“Wouldn’t you...?”

“What?”

She looked down at the ground again and blushed. At first he thought he was seeing things. Surely adults don’t blush like that? But Rebecka Mattson from Switzerland, who looked like seven million dollars, went red like a little schoolgirl.

“Wouldn’t you like to invite me to your place instead, for a glass of wine or two?” she said. “That would be nicer.”

“Well...” He hesitated.

He badly needed to sleep, to be in good shape for tomorrow. Yet he said:

“Of course. I’ve got a bottle of Barolo in the wine rack,” and for a second he thought something exciting might be about to happen after all, as if he were about to embark on an adventure.