10 August 2019 | New Scientist | 41However, Woltman says Laroche had tested
just four numbers before he struck gold.
But when it comes to the allure of giant
primes, practical value is beside the point.
Mathematicians treasure them because
they are exquisite. Caldwell likes to compare
Mersenne primes to giant diamonds.
“Probably the most practical use for diamonds
is diamond dust on blades and drills,” he says.
“The same is true of primes. The small ones
are used everywhere in encryption. But the
really big ones, they’re museum pieces.”
The most devoted prime hunters see
themselves as part of a collective enterprise,
pushing out to the furthest reaches of the
number line in search of these rare gems.
Which probably explains why Pace is
anything but exasperated by Laroche’s
lucky break. “I was happy for him,” he says.
“OK, it took me 14 years and he found one
in just four months. Can you believe that!
But I have tested thousands of candidates
over the years, so every time a new prime is
discovered I always feel I had a hand in it.” ❚of primes along the number line predicted
that there would be just three between
220,000,000 and 285,000,00. But GIMPS
has turned up 12. “Theoretically, life can be
different the further out you go,” says Chris
Caldwell, a mathematician at the University
of Tennessee and long-time GIMPS volunteer.
The implication is that we might find new
mathematical patterns.And the GIMPS software itself also happens
to have its uses for people with no interest
in numbers. It is sufficiently demanding
that many volunteers use it to stress test
their custom-built computers. Indeed, that is
exactly what Patrick Laroche of Ocala, Florida,
was doing late last year when one of his
souped-up machines discovered the 51st
Mersenne prime – the biggest yet. Laroche
didn’t want to generate interest in the search
for primes, preferring to keep a low profile.Daniel Cossins is a staff
features writer at New
Scientist. His favourite
prime number is 7enough, in 2005, after eight years of number
crunching, Cooper’s army of machines
discovered the 43rd Mersenne prime.
Cooper has since found another three of
them, the latest confirmed in 2016. The last
of these had been calculated in 2013, but the
automated system used by GIMPs to alert its
volunteers failed so the discovery only came
to light three years later, when the server’s
administrator came across it during routine
maintenance. “It was almost the lost prime,”
says Cooper.
For him, each discovery is a moment to
savour his place in the long tradition of prime
hunters, from Euclid and Euler through to
Lucas, whom he regards as an idol. “The fact
that we do it on computers rather than by
hand, as Lucas did, does sort of take the
romance out of it,” he says. “But I figure there
is a romance in the fact that pretty much
anybody can do this now.”
Pace, who took the record for the largest
prime from Cooper in 2018, echoes the
sentiment. “I don’t have a huge amount
of computing power,” he says. “Most of the
computers I’ve volunteered are just ordinary
desktop PCs. My mother is running this
program on hers. She has no idea.”
It seems a good way to use otherwise
wasted computing power. Considering that
RSA encryption – one of the standard ways
to keep your data safe online – requires
your bank to come up with two big primes
and multiply them together, finding new
numbers for this might appear useful.
Especially because it is the difficulty of
factoring the resulting product that keeps
hackers at bay. But the primes we already
know are plenty big enough for the job, so
the ones GIMPS is finding aren’t needed.
You might also think that identifying new,
giant Mersenne primes could help us solve
some perplexing mathematical riddles. But
here too, a new prime is no help. It won’t
weigh in on the twin primes conjecture, for
example, which ventures that there are an
infinite number of primes separated by 2, like
11 and 13. Nor will it prove the most famous
conjecture associated with Mersenne primes,
namely that there are infinitely many of them
too. “It doesn’t answer the question ‘but is
there another, even larger, Mersenne prime?’,”
says Vicky Neale, a mathematician at the
University of Oxford. In maths, proof comes
not from observations but self-contained
explanations based on mathematical logic,
like the one Euclid devised for infinite primes.
GIMPS has thrown up one curiosity, though.
The formula used to work out the distribution
1588
The Italian mathematician Pietro Cataldi
discovered that the number
524,287 was prime.
It would remain the largest known
prime for nearly two centuries18th century
Leonhard Euler found several new primes1951
At the dawn of the computer age, much
larger primes began to be identified1996
The Great Internet Mersenne Prime Search
was launched. Most of the largest primes
known today are Mersenne primesLength in digits (log scale)2018
Patrick Laroche discovered the
longest prime number, which has
24,862,048 digitsYe a r1600 1700 1800 1900 2000SOURCE: PRIMES.UTM.EDUPrime targets
Very small prime numbers have been known since antiquity, but as computing
has developed we have found much larger ones107106105104103102101100“ It took me 14 years
and he found one
in just four months.
Can you believe it!”