10 August 2019 | New Scientist | 39

n 2s multiplied together (where n can be any

whole number), minus 1. Mersenne primes

are Mersenne numbers that are also prime.

So, for example, the number 3 is a Mersenne

prime because it is 1 less than 2^2 , which is 4.

Seven is another because it is 1 less than 2^3.

The next few are 31, 127, 8191 and 131071,

but they quickly get much rarer. We had found

only 49 Mersenne primes before Pace snared

the 50th, most succinctly written as 2^77232917 -1.

People call it M77232917 for short.

“When I first found out, I thought it was a

joke,” says Pace. The computer that discovered

it isn’t a powerful one. Pace built it himself for

his local church, primarily for word processing,

using a mid-market processor. But once the

discovery was announced, even Pace’s children

were impressed. “At first my kids were like ‘OK,

dad’,” says Pace. “But when my son found out

National Public Radio wanted to interview me,

he suddenly thought it was cool.”

Part of the reason Mersenne primes are

considered sufficiently beguiling to pique

media interest is that they are closely related

to perfect numbers: those numbers that are

equal to the sum of all the positive numbers

you can multiply together to produce them

(excluding the number itself). The number 6,

for example, is a perfect number because it

is a product of 1 × 6 and 2 × 3, and 1 + 2 + 3 = 6.

So is 28, because 1 + 2 + 4 + 7 + 14 = 28. Because

every even perfect number can be generated

from a Mersenne prime, the two sets of

numbers are intimately connected.

The call of

the primes

Across the planet, a handful of number hunters have

an extraordinary goal: to find the biggest primes.

Daniel Cossins meets them

J

ON PACE had spent 14 years searching for

a monster. A finance manager at FedEx

in Memphis, Tennessee, he was more

comfortable trawling through spreadsheets

than hunting exotic beasts. He also happened

to be one of the least well-equipped in the

game, so he knew the odds were stacked

against him. “I probably had a better chance

of being struck by lightning,” he says.

But on 26 December 2017, Pace finally laid

eyes on the object of his desire: the largest

prime number then known, running to a

whopping 23 million digits. It was so long

that, printed out in two-point font, it could

have easily filled a book.

In some ways, he needn’t have bothered.

His discovery has virtually no practical value.

So what has inspired Pace and hundreds of

others to devote themselves to the Great

Internet Mersenne Prime Search (GIMPS), in

which people scour the furthest reaches of the

number line in search of enormous primes?

There is no one single answer. Not all the

volunteers are numberphiles. Some get into it

for the prize money offered for innovations in

computing: $150,000 for the first 100-million

digit prime. Others join the hunt to put their

latest souped-up computer through its paces.

For the most devoted, though, it is above all

about the thrill of discovering something

rare and beautiful, something nobody has

ever seen before.

Primes, for those in need of a quick primer,

are the numbers greater than 1 that are

divisible only by 1 and themselves. The

sequence begins 2, 3, 5, 7, 11, 13, 17 and goes on

infinitely, as ancient Greek mathematician

Euclid showed in a beautiful proof in around

300 BC. They are cherished as the fundamental

building blocks from which all numbers are

made, because any number that isn’t prime

can be made by multiplying primes together.

What Pace found is not just any prime. It is in

a special class known as the Mersenne primes,

named after Marin Mersenne, a 17th-century

French friar. Mersenne numbers are 1 less than

a power of 2. They can be written in the form

of 2n-1, which means the number is equal to

>

To join the hunt for Mersenne

primes, go to mersenne.org and

set up an account. There, you

can download a program called

Prime95. It has versions for most

types of computer. Once installed,

it will run in the background, using

any spare processing power. You

won’t notice it. If your computer

finds anything, you will get an email

letting you know — and asking you

to keep it under your hat until it is

publicly announced.

HOW TO BECOME A

NUMBER HUNTER