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Authors: Yōko Ogawa
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known examples, or twin primes, or the Mersenne
primes—the slightest change in the shape of his argument could
make you see something you had never understood before. Even a
difference in the weather or in his tone of voice seemed to cast
these numbers in a different light.
To me, the appeal of prime numbers had something to do with
the fact that you could never predict when one would appear. They
seemed to be scattered along the number line at any place that took
their fancy. The farther you get from zero, the harder they are to
find, and no theory or rule could predict where they will turn up
next. It was this tantalizing puzzle that held the Professor captive.
"Let's try finding the prime numbers up to 100," the Professor
said one day when Root had finished his homework. He took his
pencil and began making a list: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
It always amazed me how easily numbers seemed to flow from
the Professor, at any time, under any circumstances. How could
these trembling hands, which could barely turn on the microwave,
make such precise numbers of all shapes and sizes?
I also liked the way he wrote his numbers with his little stub of
a pencil. The 4 was so round it looked like a knot of ribbon, and
the 5 was leaning so far forward it seemed about to tip over. They
weren't lined up very neatly, but they all had a certain personality.
The Professor's lifelong affection for numbers could be seen in
every figure he wrote.
"So, what do you see?" He tended to begin with this sort of
general question.
"They're scattered all over the place." Root usually answered
first. "And 2 is the only one that's even." For some reason, he always
noticed the odd man out.
"You're right. Two is the only even prime. It's the leadoff batter
for the infinite team of prime numbers after it."
"That must be awfully lonely," said Root.
"Don't worry," said the Professor. "If it gets lonely, it has lots of
company with the other even numbers."
"But some of them come in pairs, like 17 and 19, and 41 and
43," I said, not wanting to be shown up by Root.
"A very astute observation," said the Professor. "Those are
known as 'twin primes.' "
I wondered why ordinary words seemed so exotic when they
were used in relation to numbers. Amicable numbers or twin primes had a precise quality about them, and yet they sounded as though
they'd been taken straight out of a poem. In my mind, the twins
had matching outfits and stood holding hands as they waited in
the number line.
"As the numbers get bigger, the distance between primes increases
as well, and it becomes more difficult to find twins. So we
don't know yet whether twin primes are infinite the way prime
numbers themselves are." As he spoke, the Professor circled the
consecutive pairs.
Among the many things that made the Professor an excellent
teacher was the fact that he wasn't afraid to say "we don't know."
For the Professor, there was no shame in admitting you didn't
have the answer, it was a necessary step toward the truth. It was as
important to teach us about the unknown or the unknowable as it
was to teach us what had already been safely proven.
"If numbers never end, then there should always be more
twins, right?"
"That makes sense, Root. But when you get to much bigger
numbers—a million or ten million—you're venturing into a wasteland
where the primes are terribly far apart."
"A wasteland?"
"That's right, a desert. No matter how far you go, you don't
find any. Just sand as far as the eye can see. The sun shines down
mercilessly, your throat is parched, your eyes glaze over. Then you
think you see one, a prime number at last, and you go running
toward it—only to find that it's just a mirage, nothing but hot
wind. Still, you refuse to give up, staggering on step by step,
determined to continue the search ... until you see it at last, the
oasis of another prime number, a place of rest and cool,
primes—the slightest change in the shape of his argument could
make you see something you had never understood before. Even a
difference in the weather or in his tone of voice seemed to cast
these numbers in a different light.
To me, the appeal of prime numbers had something to do with
the fact that you could never predict when one would appear. They
seemed to be scattered along the number line at any place that took
their fancy. The farther you get from zero, the harder they are to
find, and no theory or rule could predict where they will turn up
next. It was this tantalizing puzzle that held the Professor captive.
"Let's try finding the prime numbers up to 100," the Professor
said one day when Root had finished his homework. He took his
pencil and began making a list: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
It always amazed me how easily numbers seemed to flow from
the Professor, at any time, under any circumstances. How could
these trembling hands, which could barely turn on the microwave,
make such precise numbers of all shapes and sizes?
I also liked the way he wrote his numbers with his little stub of
a pencil. The 4 was so round it looked like a knot of ribbon, and
the 5 was leaning so far forward it seemed about to tip over. They
weren't lined up very neatly, but they all had a certain personality.
The Professor's lifelong affection for numbers could be seen in
every figure he wrote.
"So, what do you see?" He tended to begin with this sort of
general question.
"They're scattered all over the place." Root usually answered
first. "And 2 is the only one that's even." For some reason, he always
noticed the odd man out.
"You're right. Two is the only even prime. It's the leadoff batter
for the infinite team of prime numbers after it."
"That must be awfully lonely," said Root.
"Don't worry," said the Professor. "If it gets lonely, it has lots of
company with the other even numbers."
"But some of them come in pairs, like 17 and 19, and 41 and
43," I said, not wanting to be shown up by Root.
"A very astute observation," said the Professor. "Those are
known as 'twin primes.' "
I wondered why ordinary words seemed so exotic when they
were used in relation to numbers. Amicable numbers or twin primes had a precise quality about them, and yet they sounded as though
they'd been taken straight out of a poem. In my mind, the twins
had matching outfits and stood holding hands as they waited in
the number line.
"As the numbers get bigger, the distance between primes increases
as well, and it becomes more difficult to find twins. So we
don't know yet whether twin primes are infinite the way prime
numbers themselves are." As he spoke, the Professor circled the
consecutive pairs.
Among the many things that made the Professor an excellent
teacher was the fact that he wasn't afraid to say "we don't know."
For the Professor, there was no shame in admitting you didn't
have the answer, it was a necessary step toward the truth. It was as
important to teach us about the unknown or the unknowable as it
was to teach us what had already been safely proven.
"If numbers never end, then there should always be more
twins, right?"
"That makes sense, Root. But when you get to much bigger
numbers—a million or ten million—you're venturing into a wasteland
where the primes are terribly far apart."
"A wasteland?"
"That's right, a desert. No matter how far you go, you don't
find any. Just sand as far as the eye can see. The sun shines down
mercilessly, your throat is parched, your eyes glaze over. Then you
think you see one, a prime number at last, and you go running
toward it—only to find that it's just a mirage, nothing but hot
wind. Still, you refuse to give up, staggering on step by step,
determined to continue the search ... until you see it at last, the
oasis of another prime number, a place of rest and cool,
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