Using a computer powered by an off-the-shelf Intel Core i5-6600 processor, a FedEx employee from Tennessee has discovered the largest prime number known to humanity. At 23,249,425 digits long, it’s nearly a million digits longer than the previous record holder.

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A prime number is any number that can only be divided by one and itself (e.g. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc.). It’s a freaky quirk of the Universe that has captivated mathematicians for centuries, as their appearance in the roll call of all integers defies prediction (though biases have been detected in the distribution of consecutive primes).

Finding prime numbers thus requires a bit of trial-and-error, patience and a lot of computing power.

The new record-holding prime number, dubbed “M77232917”, was discovered by Jonathan Pace, a 51-year-old electrical engineer living in Germantown, Tennessee, on December 26, 2017. It was discovered as part of the Great Internet Mersenne Prime Search (GIMPS), a group that does exactly what its name implies.

Mersenne primes — named after the 17th century French monk Marin Mersenne — are a rare class of primes that are one integer less than a number that’s been multiplied by itself, expressed as *M _{n}*=2

^{n}-1. In this case, the new prime was calculated by multiplying 77,232,917 by 77,232,917 and then subtracting one (2

^{77,232,917}-1). The new prime is the 50th known Mersenne prime.

M77232917 contains 23,249,425 digits, which is practically impossible for the human brain to comprehend. You can download a zip file of the number here, which busts open into a simple text file nearly 24 MB in size. Here’s an itsy-bitsy, teeny-tiny glimpse of the first few digits of the number:

467333183359231099988335585561115521251321102817714495798582338593567923480521177207484311099740208849621368090038049317248367442513519144365249220286787499224923639633038619305951170770522850356011779638644050954128274109548519743273551014325753249976993808191641040774990607027085131780854431482719287927051574760059182501122426493901177524147020112211388180246357120385256971031180861489618892584067750976814954567907442159253928086043451513107052318572800622535173305043931545049276946896285268869674944342112985792233732337801754241421827174125670264416644353313890442672256181107628062641550510992384203991225537857049225867450478199850186985188395719963008038717965906943698446227245769048442624077040456516926390008651726462990593760595429486791654633562139216744557672746497884434353520456556797052450980481438931349795938877105350614496693489409255155953306872814733490045565082856578190868933327141046378794972655266893887595979641316331028806592177529769834152124115913323365268166706644473143310974520823513974885636253719301950406605722095718079173467784212323941225708492276162678848504240175619575042958633387070067162448853074807881260125089824549619209919961134580250514604063519606634978181198613503051581163463555633566319896615827604388690329796011984096270537383579630874681056843649818067678103424096859574594387122476571828072557344394780380024201783548667495179746696190843622986643959450031252516686566594252074345358101581042723707992427571828820948849065861590065859074391377828173034683701925114789618787309101887004289046129873028746416386957443644028588809312429908860884297613860386816910586542216739001402734982971907272987483662107236827512472738409809578930670626153249685719278922751692157130896802807496462527584643633045876649970923366331569812027362273631245871521356011614860439988085178768763757860732625585115457092087848043258257876286498706458088135038948822247351807130888403164645794446319243717913259933477001220994458815795663730102285010141814663265537150923894600650386095599714691658518044760943228485293103850039495787904594766307709643249139518714435912361386106141359015789488893140142052513122486651646114701666701676143140750087224603889234655205528086110973730635187042131130393016253362794058251836128055518549678930658366455272915511811952058888392595313861166137697724678782720586680474567342842176857469092018559835324800004598444782456084485904576297338813661199170205858652099033435737405594286587479579072034591348880491778480562894857788046177321792968258171597503720079791566992083055824866579012557180722751078462924794248439652077467237403658550061799279956704411031254567465451105499362798947781210188466981867175415780089815289984924792655784203471522023573618649847743212240495339397953595778060553510296261735673554034489108685389266344608133903535814448582274184496823988891485433908407138755118440965780608756502239030483891349117815030583034147983474364473410786162232983781676844315610390028354503758000566280031377558992067117024880997033717503400673301922738074511864300037419291160271133918403435581992793701952141372100135595457599485254674121618690682674413645774237169049255424728665357996103997069776243968010876776475830443576635739972027953438424843103674054245431824410173440025375378765370235220916664367509996157398715673180804853549565098667607871303308044944405283848532769455954881164266322865068561846182186079278726212101078949803932341590437977436216839406044542808714268030063768857675412060494935032858614372477002463478278523399030686898768798513296184049579718910789231320899515797161738788846785311885…

You get the point.

According to GIMP, that’s big enough to fill an entire shelf of books totalling 9,000 pages. Or put another way, “If every second you were to write five digits to an inch then 54 days later you’d have a number stretching over [118km] — almost [5km] longer than the previous record prime,” writes GIMP.

Pace, a long-time maths enthusiast and a current employee at FedEx, does charity work as a SysAdmin, running Prime95 on all his PCs and servers; Pace is one of thousands of volunteers who are using free GIMPS software in the effort to continually find larger and larger prime numbers. The PC that Pace used to find the prime number required six straight days of computation on a quad-core Intel i5-6600 CPU to verify it.

Indeed, the discovery of new primes is no small task; every candidate prime must go through the time-consuming and rigorous process of being cut-up by any potential divisors. Once a candidate prime is discovered, it has to be verified by outside sources. In this case, the prime was independently verified by four different programs running on different hardware configurations:

- Aaron Blosser verified it using Prime95 on an Intel Xeon server in 37 hours.
- David Stanfill verified it using gpuOwL on an AMD RX Vega 64 GPU in 34 hours
- Andreas Höglund verified the prime using CUDALucas running on NVidia Titan Black GPU in 73 hours
- Ernst Mayer also verified it using his own program Mlucas on 32-core Xeon server in 82 hours. Andreas Höglund also confirmed using Mlucas running on an Amazon AWS instance in 65 hours.

The quest to find more prime numbers may seem frivolous, but they hold practical applications as well, such as the generation of public key cryptography algorithms, hash tables, and as random number generators. Further work into primes could also tell us a bit more about mathematics and why it’s so damned good at describing the universe.

And as Carl Sagan speculated in *Cosmos*, transmitting streams of consecutive primes could also be used as a way of saying “hello” to an alien civilisation.

As exciting as this discovery is, the Holy Grail of primes is yet to be found: a prime number containing 100 million digits. The first person to find this elusive number will be awarded $US150,000 ($191,107) by the Electronic Frontier Foundation. Good luck!

[Mersenne]