Forty-three of them, printed between the digits. Each begins
in real mathematics and then keeps going, into the person it happened to.
IFirst Things5 stories
01The Bone That Countedp. 8
Twenty thousand years ago, someone cut three columns of notches into a baboon's fibula, and one column contains every prime between ten and twenty, in order. Fixed into one end is a sliver of quartz, which means the oldest object ever accused of doing mathematics may also be the pen.02Euclid's Three Immortal Linesp. 13
The oldest machine still in service has no moving parts and has never been down for maintenance: hand it every prime ever found and it proves your list is incomplete. It is so simple that people routinely improve it into being wrong.03The Librarian's Sievep. 19
His colleagues nicknamed him Beta — second-best at everything — and he found a way to catch every prime in a range by refusing to look for any of them. Twenty-two centuries later the ritual is still being performed, correctly, in rooms nobody is in.04When 1 Was Primep. 27
The most authoritative prime table ever compiled by hand, published in 1914, begins with the number 1. Nothing about 1 has changed since; what changed was the paperwork.05The Atoms of Arithmeticp. 30
Every number comes apart into primes exactly one way, which is the load-bearing wall of arithmetic — and for two thousand years nobody bothered to say so out loud. Then, in the 1840s, mathematicians built a number system where it stopped being true, and watched a famous proof collapse in public.IIObsessives & Originals6 stories
06Fermat's Beautiful Mistakep. 38
He checked five numbers, got five primes, and declared the pattern infinite. The sixth is composite, and the wreckage of that one bad forecast handed Gauss a two-thousand-year-old geometry problem.07Monsieur Le Blancp. 41
A student at the École Polytechnique kept submitting extraordinary work despite never attending, never sitting an exam, and — it turned out — not existing. Years later she talked a French general into protecting Gauss from an advancing army, and Gauss replied that he had never heard of her.08The Friar Who Ran the Internet of 1640p. 46
European science had one node, and it was a monk's cell in Paris. From it he published fifty-five verdicts on numbers nobody alive could check; the grading took three centuries and he got fifty right.09The Champion and the Dinner Platep. 53
A Paris schoolteacher spent nineteen years of evenings proving a thirty-nine-digit number prime, and set a record that stood for seventy-five. He was killed by a shard from a dropped dinner plate.10The Duelist's Last Nightp. 56
With a duel at dawn he could not expect to survive, a twenty-year-old spent the night writing out his mathematics, scrawling there is no time in the margins. He lies in an unmarked grave nobody can find; his estate is executed a few billion times a day at checkout counters.11The Job Offer That Arrived Two Days Latep. 62
In Berlin, a publisher sat down to write the best letter of his life: a salaried professorship for the most gifted mathematician alive. Every word was true, and the young Norwegian had died two days earlier.IIIThe Great Unsolved5 stories
12The Boy Counting Primesp. 67
A fifteen-year-old started tallying primes in the back pages of a logarithm table, in idle quarter-hours, and found the hidden statistical law governing them. He told almost no one for fifty-seven years, and watched someone else take the credit.13Teatime at the Institutep. 70
A number theorist described his formula for how the primes' hidden frequencies space themselves, and the physicist across the tea room finished the sentence for him — he had derived the same expression for the energy levels of heavy atomic nuclei. No one has ever explained why they match.14The Man From Nowherep. 75
A fifty-eight-year-old calculus lecturer with almost no publications sent the world's most exclusive journal a solution to a problem generations of the best had failed. It cleared review in three weeks; he had spent seven of the intervening years keeping the books for a Subway franchise.15The Liarsp. 82
Certain composite numbers pass the classic test for primality against every witness, lying so convincingly that no serious system trusts that test alone. The twenty-seven-year-old hole in what was known about them was closed by a high-school senior who got interested by watching a documentary.16Six Square Metersp. 86
A room in Beijing with a bare bulb, a bed, no desk, and a man working with a board across his knees, keeping his finished calculations in sacks. Measured by output per square foot, it was the most productive workspace of the twentieth century.IVMachines & The Great Hunts6 stories
17The Bicycle-Chain Computerp. 92
In 1926 a Berkeley student built a working computer out of bicycle chains, each cycling at its own period until every marker surfaced at once. Every prime hunt running tonight still uses the two-stage design he inherited from his father and refined with his wife, whose name the university rules kept off the door.18Two Before Midnightp. 99
In 1951 the last record set by human hand and the first set by machine happened weeks apart, and no document on either side can settle which came first. The argument stopped mattering the following January, when a man who had never programmed a computer found two world records before midnight on his first attempt.19Turing's Gearsp. 105
In 1939 he asked the Royal Society for forty pounds, mostly for gear blanks, to build a machine that would listen to the hidden frequencies of the primes. The money was approved, the gears were cut, and then the war arrived.20The Prime Nobody Noticedp. 108
On a Thursday in September, a lab computer in Missouri found the largest prime number known to the human race, sent the standard notification, and moved on to its next assignment. For one hundred and twelve days, nobody opened the email.21The Man Who Found This Bookp. 114
The same man has found the largest known prime on Earth four times, and every one of those records is now gone. The number in your hands is the one his machines certified in 2006 and nobody, including him, ever had a reason to look at again.22The Lava Lamps That Feed the Primesp. 118
A wall of a hundred lava lamps in a San Francisco lobby is on the security payroll, filmed continuously, because computers are terrible at being unpredictable and cryptographic secrets have to be born from chaos. The man who invented the idea had, as a high-school student in 1978, held the record for the largest known prime.VCodes & Crimes6 stories
23The Trapdoor That Runs the Worldp. 129
For a year two men invented locks and a third broke every one of them, dozens in all. When one finally held, the breaker judged it the least important paper he would ever have his name on and asked to be listed last — which is why the acronym ends in A.24Forty Quadrillion Yearsp. 137
In 1977 a magazine offered a hundred dollars to anyone who could read one sentence, along with the arithmetic showing it would take forty quadrillion years. It took seventeen, six hundred strangers, and sixteen hundred machines — two of which were fax machines.25The Illegal Numberp. 144
When courts ordered a magazine to stop publishing a piece of banned code, a programmer went hunting near the number that code becomes when you read it as an integer. He found a certified 1,401-digit prime that unpacks into the forbidden program, and filed it in the public mathematical record.26The Professor Who Broke Intelp. 147
A professor grinding through trillions of twin primes on a question with no commercial value spent months trying to prove he was the broken part. He wasn't, and the interval between what the company knew and what it said cost it $475 million.27The Killer's Period Nineteenp. 155
A killer's 340-symbol cipher defeated the FBI, the Navy and fifty-one years of professionals, until three hobbyists on three continents found the message was read on a diagonal stepping by nineteen. Then they read what it said, and it named nobody.28The Quantum Deadlinep. 161
Somewhere on hardware nobody advertises, encrypted files no machine can currently read are being stored anyway, at expense, by people willing to wait. The deadline is not when the machine arrives; it is that date minus how long your secrets have to keep.VIThe Invisible Infrastructure4 stories
29The Prime Behind a Billion Messagesp. 170
The most widely used prime in the world is seventy-seven digits long, invoked billions of times a day, and almost nobody has ever seen it. Its real story is not mathematics but the question every standards body faced after 2013: how do you prove you didn't rig your own numbers?30The Prime Under Every Bitcoinp. 173
For over a decade a man in Wales has been petitioning his council to let him dig up a landfill, at his own expense, for a hard drive holding a number he can no longer remember. The system agrees the coins are his; it has no procedure by which that can matter.31The Bitcoin in the Popcorn Tinp. 177
Federal agents searching a house in Georgia found a tin of popcorn in a bathroom closet, and under the blankets inside it, a hobbyist computer holding $3.36 billion. It had sat there nine years, in plain view of every investigator on earth.32Fifteen on Seven Qubitsp. 182
In 2001 the most advanced computer in the world was a test tube, and it was asked to factor 15. Twenty-five years later, no machine has independently factored a number a child couldn't — and the deadline is still getting closer, from a direction nobody watches.VIIPrime Rhythms3 stories
33The Cicadas' Calendarp. 189
Seven species of periodical cicada, and every one runs on thirteen or seventeen years — no twelves, no sixteens. They have no clock underground; they count trees, and researchers proved it by fooling one into emerging a year early.34Music for the End of Timep. 194
In a Silesian prison camp in January 1941, four prisoners premiered a quartet written for the instruments that happened to be in the room. Beneath the first movement, seventeen durations turn against twenty-nine chords, a pattern that cannot realign until long after the music ends.35Five Legs, One Fusep. 198
Handed a piece of film showing nothing but a burning fuse, a composer wrote a theme in five beats to the bar — a meter that cannot be split in half and never lets the listener settle. In 1996 somebody re-recorded it squared up to four, and proved the point by ruining it.VIIIPatterns & Signals2 stories
36First Words to the Starsp. 207
In 1974 humanity sent 1,679 bits toward a cluster twenty-five thousand years away, with no key, no header, and nothing to say a message was what it was. The first thing it communicates isn't in the message — it's in the fact that 1,679 factors exactly one way.37The Doodlep. 214
Bored at a long meeting in 1963, a man spiralled the integers outward on scratch paper and circled the primes, and something appeared that had no business being there. The most famous image in number theory was a byproduct of not listening.IXThe Overlooked3 stories
38The Twins Who Spoke in Primesp. 224
A neurologist watched two institutionalized twins trade six-figure primes back and forth with a secret smile, and wrote it up nineteen years later — describing a table of primes that could not have existed. What nobody disputes is that they were separated for their own good, and never did it again.39Half of Forty-Fivep. 232
A boy figured that if he could be half as good as his older brother, who wore 45, he'd have done all right — and a jersey being a jersey, he rounded up to 23. The theory that great athletes are drawn to indivisible numbers survives about ninety seconds of checking.40Pick 199p. 237
The most thorough talent evaluation in American life, hundreds of scouts and millions of dollars, put the best player in the sport's history 199th. Every measurement was accurate; every column was right; the conclusion was wrong by the widest margin the game has seen.XThe Playful Cabinet3 stories
41Belphegor's Primep. 245
Thirty-one digits: a 1 at each end, thirteen zeros on each side, and 666 in the middle. It has been called cursed and printed on T-shirts, and every ominous thing about it disappears the moment you write it in another base.42The Sheldon Primep. 251
In 2010 a sitcom character rattled off fifteen seconds of reasons that 73 is the best number, and every claim was true. Nine years later one of the most distinguished number theorists alive proved that in the infinite sequence of primes, there is exactly one like it.43Take Fifty-Sevenp. 259
Asked to make an abstraction concrete by naming an actual prime, the greatest mathematical mind of his century paused and said 57. Fifty-seven is 3 × 19, and mathematicians have called it the Grothendieck prime ever since — with something closer to tenderness than embarrassment.
Page numbers are the printed folios of the hardcover
edition.