‘OK, well this is going to sound totally nuts, but there are lots of numbers on that bill, not just the serial number. The letters, they could represent values, too. And then,’ he finished his own coffee, ‘there is something special on the reverse. This is actually exciting. Let me show you.’

‘What, here?’

‘Yes, why not?’

‘Because … Oh, fuck it.’ I dug the note out of my pocket and unfolded it flat on its front. ‘There aren’t any numbers on the back – apart from 100, of course.’

‘No, you see,’ he pointed to the blank white space on either side of the words ‘IN GOD WE TRUST’ cut in two by the spire of Independence Hall. ‘There are ones and zeros written in yellow. Twenty-four of them on the left, twenty-one of them on the right.’

‘Are you sure they’re numbers,’ I asked him, ‘and not just marks?’

‘There’s no difference. A mark is a number, if you ascribe a value to it. I told you it was exciting.’

‘If you say so.’ I folded the note away again and picked up the cigarettes. ‘Exciting how, anyway?’

‘How?’ His fingers drummed the table. ‘It’s like I told you in Paris. Ones and zeros. It’s binary!’

‘So …?’ He shook his head as if I was mentally incapacitated in some vital respect.

‘So, Rachel is a computer scientist. Writing in binary values is what she does. One, zero. On, off. Yes, no.’

‘Baaz?’ He looked at me, eyes wide with unfathomable possibilities. ‘There are billions of hundred-dollar bills out there in the world.’ I pointed towards the window. ‘And, you know, quite a few computer scientists, too. So …’

‘But there are not billions of hundred-dollar bills out there with that serial number, connected to one of the world’s leading computer scientists. What is the probability of that?’

‘Small,’ I admitted.

‘Small? It’s statistically impossible. And please don’t tell me that she fancied you, because you are totally rubbish at mathematics.’

I let that go.

I wondered if his professor had also warned him of the dangers of looking for false positives.

‘OK. Let’s assume you’re right. Back to my original question: what do you think it means?’

‘Probably nothing.’ He smiled at me and sat back in his chair. I made a strenuous effort to keep my hands on the table and not put them around his neck. ‘But prime factorization is extremely important in cryptography,’ he said, sensing my frustration.

‘Cut me some slack, Baaz.’

‘OK. You multiply one prime by another. The result is a semiprime, and that number secures the encryption. In order to break it, you’d need to know the numbers that were multiplied in the first place. It’s very fast to multiply two large prime numbers and get the result. But it’s unbelievably computer-intensive to do the reverse. Especially if you have a big prime.’

‘How big?’