Maths fans can’t get enough of numbers that are millions of digits long and can only be divided by themselves and one. Now, through a collaborative effort, utilising computers distributed around the world, they’ve discovered that the number 277,232,917 – 1 is prime.

The discovery was initially made on 26th December by a computer volunteered by Jonathan Pace, as part of the Great Internet Mersenne Prime Search (GIMPS). Pace, a 51-year old electrical engineer based in Germantown, Tennessee, has been hunting primes for over fourteen years and his belated Christmas present is eligible for a $3,000 reward from GIMPS.

The new prime number, known as M77232917, is one million digits larger than the previous record. It is also a particularly rare type of prime called a Mersenne prime, meaning that it is </s> An electrical engineer in Germantown, Tennessee, has been searching for big prime numbers for the last 14 years, as a volunteer who uses his computer to run a software designed to do exactly that. In late December, Jonathan Pace, 51, struck gold when his machine pumped out the largest known prime number yet.

What is this number? Well, since it clocks in at a humongous 23 million digits long, writing it down in its entirety, five digits to an inch, would require over 73 miles of space. And at the speed of five digits written every second, writing the number out would take 54 days, without any breaks. So no, that number itself won’t be written out in full here.

However, it is the result you get if you multiply the number 2 by itself 77,232,917 times, and then subtract 1 from it. So that you don’t have to go through the process of verifying it for yourself, an online collaboration called Great Internet Mersenne Prime Search (GIMPS) — whose software Pace was running — already did that.

The number was discovered Dec. 26, but GIMPS made the announcement Wednesday, having spent the intervening time running “four different programs on four different hardware configurations” to confirm proof of primality.

The newly discovered number has exactly 23,249,425 digits and is called M77232917, since it also belongs to a rare class of prime numbers called Mersenne primes. These numbers are always 1 short of a multiplication of 2s. For instance, the first Mersenne prime is 3 (2x2-1), the next is 7 (2x2x2-1), after that is 31 (2x2x2x2x2-1) and so on.

The new addition to the Mersenne primes is the 50th number of its kind to have been found, and it beat the previous largest known prime number, also a Mersenne prime, by 910,807 digits. That number was also found by the GIMPS collaboration, in January 2016. In terms of writing it down, the 49th Mersenne prime would be about 3 miles shorter than its successor.

Mersenne primes are named in honor of Marin Mersenne, a French friar who studied them almost four centuries ago.

For his efforts, Pace won a $3,000 GIMPS research discovery award. If you would like to have a chance of winning another such award in the future, you can volunteer with GIMPS by installing its free software on your computer and running it in the hope of finding the next Mersenne prime. The program can be downloaded using this link.

GIMPS hopes to win the $150,000 award, announced by the Electronic Frontier Foundation, for discovering the first prime number with over 100 million digits. There is also a $250,000 award for finding the first billion-digit prime number.

Really big prime numbers don’t have many practical uses yet, but cryptography algorithms based on prime numbers have been developed. </s> At more than 23m digits long, the number is something of a beast. But for mathematicians, the latest discovery from a global gang of enthusiasts is a thing of beauty: the largest prime number ever found.



Known simply as M77232917, the figure is arrived at by calculating two to the power of 77,232,917 and subtracting one, leaving a gargantuan string of 23,249,425 digits. The result is nearly one million digits longer than the previous record holder discovered in January 2016.



The number belongs to a rare group of so-called Mersenne prime numbers, named after the 17th century French monk Marin Mersenne. Like any prime number, a Mersenne prime is divisible only by itself and one, but is derived by multiplying twos together over and over before taking away one. The previous record-holding number was the 49th Mersenne prime ever found, making the new one the 50th.



“I’m very surprised it was found this quickly; we expected it to take longer,” said Chris Caldwell, a professor of mathematics who runs a website on the largest prime numbers at the University of Tennessee at Martin. “It’s like finding dead cats on the road. You don’t expect to find two so close to one another.”



The new prime number was originally found on Boxing Day by the Great Internet Mersenne Prime Search (Gimps) collaboration which harnesses the number-crunching power of volunteers’ computers all over the world. In the days after, four more computers sporting different hardware and software were set the task of verifying the discovery. Those computers confirmed the result, taking between 34 and 82 hours each.

To find M77232917 in the first place took six full days of nonstop computing on a PC owned by Jonathan Pace, a 51-year old electrical engineer from Germantown, Tennessee. It is the first prime that Pace’s computer has churned out in 14 years on the Gimps project. He is now eligible for a $3,000 award.

When asked about mathematicians’ fascination with such mammoth numbers, Caldwell said: “They are exciting to those of us who are interested in them. It’s like asking why do you climb a mountain.” He compares prime numbers to diamonds, with small ones finding uses in encryption and other applications, but large ones being more like showpieces. “That’s what we’re talking about here: it’s a museum piece as opposed to something that industry would use,” he said.

Curtis Cooper, a professor of mathematics at the University of Central Missouri, found the previous record-holding Mersenne prime in 2016, the fourth prime he has helped to find through the Gimps project in 20 years. He said he was a little sad at having lost the record so soon, but added: “I’m really happy for the whole organisation and the guy who found it. He’d been searching for 14 years, so he’s worked as hard as I have.”

“Discovering new primes, which are things you can touch, it’s the realisation of my love for mathematics. That’s the appeal for me,” he said. </s> The World Has A New Largest-Known Prime Number

There's a new behemoth in the ongoing search for ever-larger prime numbers — and it's nearly 25 million digits long.

A prime is a number that can be divided only by two whole numbers: itself and 1. The newly discovered number is what's known as a Mersenne prime, named for a French monk named Marin Mersenne who studied primes some 350 years ago.

Mersenne primes have a simple formula: 2n-1. In this case, "n" is equal to 82,589,933, which is itself a prime number. If you do the math, the new largest-known prime is a whopping 24,862,048 digits long.

We would write the number out for you, but it would fill up thousands of pages, give or take, and look like this gigantic zip file.

The latest Mersenne prime comes courtesy of a project started in 1996 called the Great Internet Mersenne Prime Search, in which people download special software that runs in the background on their computers. A computer owned by Patrick Laroche of Ocala, Fla., discovered the number on Dec. 7, and mathematicians have spent the past two weeks verifying the calculations. It's more than a million and a half digits longer than the previous largest known prime, discovered about a year ago by a computer in Germantown, Tenn.

Why should you care about Mersenne primes? They've proven useful in generating reasonably random numbers, but the best answer might be simply because they're there — and they're majestic.

Chris Caldwell, a mathematician at the University of Tennessee, Martin, talked to NPR in 2009 about these large primes.

"Mersennes, in a way, are kind of like a large diamond," Caldwell said back in 2009. Think about the Hope Diamond, a 45.52-carat diamond that sits in a special case in the Smithsonian National Museum of Natural History, usually with crowds around it.

"Nobody there looking at the Hope Diamond ever asks, 'Why did they bother to dig it up?' or 'What is it good for?' — even though it really isn't good for much other than to just hang there and people to look at," Caldwell said. "And in many ways, the Mersennes play that same role — that they really are the jewels of number theory." </s> Jonathan is one of thousands of volunteers using free GIMPS software.

The new prime number, also known as M77232917, is calculated by multiplying together 77,232,917 twos, and then subtracting one. It is nearly one million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 50th known Mersenne prime ever discovered, each increasingly difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 16 Mersenne primes. Volunteers download a free program to search for these primes, with a cash award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell maintains an authoritative web site on the largest known primes, and has an excellent history of Mersenne primes.

The primality proof took six days of non-stop computing on a PC with an Intel i5-6600 CPU. To prove there were no errors in the prime discovery process, the new prime was independently verified using four different programs on four 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.

Jonathan Pace is a 51-year old Electrical Engineer living in Germantown, Tennessee. Perseverance has finally paid off for Jon—he has been hunting for big primes with GIMPS for over 14 years. The discovery is eligible for a $3,000 GIMPS research discovery award.

GIMPS Prime95 client software was developed by founder George Woltman. Scott Kurowski wrote the PrimeNet system software that coordinates GIMPS' computers. Aaron Blosser is now the system administrator, upgrading and maintaining PrimeNet as needed. Volunteers have a chance to earn research discovery awards of $3,000 or $50,000 if their computer discovers a new Mersenne prime. GIMPS' next major goal is to win the $150,000 award administered by the Electronic Frontier Foundation offered for finding a 100 million digit prime number.

Credit for this prime goes not only to Jonathan Pace for running the Prime95 software, Woltman for writing the software, Kurowski and Blosser for their work on the Primenet server, but also the thousands of GIMPS volunteers that sifted through millions of non-prime candidates. In recognition of all the above people, official credit for this discovery goes to "J. Pace, G. Woltman, S. Kurowski, A. Blosser, et al." </s> On 6/2/2018 1:27 PM, Bill Gray pluto@... [mpml] wrote:> Hi Alan,> I've just updated the impact plot to show UT times of impact :> This also reflects some new info on the astrometric uncertainties.> It assumes sigmas of 0.7 arcsec for the first four discovery observations> (which didn't track the object's motion). The next four observations> from (I52) _did_ track the object and have 0.3" assumed uncertainty;> the last four, from (G96) but tracking the motion, are at 0.5". And> a half-second timing error is assumed for all of them.> Following is the astrometry with COM keywords used to specify the> uncertainties. Use these in Find_Orb, on-line or in the Windows or> Linux flavors, and it'll "see" the COM sigma lines and set uncertainties> accordingly.> The revised sigmas expand the impact area a good bit. Impacts as far> west as Madagascar or as far east as over the International Date Line are> now entirely possible. Or even just flat-out missing us; I'm now getting> an 85% impact probability. (And Scout is still getting only a 30%> probability... I still suspect that means we have somewhat different> assumptions. Maybe in our over-observing parameters?)> If it hit at about 15:00, it would have been in New Guinea and at> H=31.7. If it hit off Madagascar at about 16:30, we'd be looking at> an H=30.7 object.> -- Bill> COD G96> COM Posn sigma 0.7> COM Time sigma 0.5> ZLAF9B2 C2018 06 02.34330 16 11 10.34 -11 19 34.7 G96> ZLAF9B2 C2018 06 02.34851 16 10 59.30 -11 20 21.6 18.2 G G96> ZLAF9B2 C2018 06 02.35373 16 10 48.15 -11 21 08.9 18.3 G G96> ZLAF9B2 C2018 06 02.35895 16 10 36.57 -11 21 57.6 18.0 G G96> COD I52> COM Posn sigma 0.3> COM Time sigma 0.5> ZLAF9B2 C2018 06 02.39785 16 09 02.60 -11 28 26.0 17.5 GUNEOCPI52> ZLAF9B2 C2018 06 02.39804 16 09 02.13 -11 28 28.1 17.2 GUNEOCPI52> ZLAF9B2 C2018 06 02.39822 16 09 01.62 -11 28 30.1 17.5 GUNEOCPI52> ZLAF9B2 C2018 06 02.39840 16 09 01.15 -11 28 31.8 17.7 GUNEOCPI52> COD G96> COM Posn sigma 0.5> COM Time sigma 0.5> ZLAF9B2 C2018 06 02.40223 16 08 51.04 -11 29 13.6 17.7 GUNEOCPG96> ZLAF9B2 C2018 06 02.40233 16 08 50.78 -11 29 15.1 17.9 GUNEOCPG96> ZLAF9B2 C2018 06 02.40242 16 08 50.58 -11 29 16.1 17.8 GUNEOCPG96> ZLAF9B2 C2018 06 02.40251 16 08 50.28 -11 29 16.8 17.8 GUNEOCPG96> On 2018-06-02 13:05, AlanCahill neoprog@... [mpml] wrote:> > Any idea of dates and timing for close approach?> > Cheers> >> > Alan> > Abbeydale Observatory (J94)> >> > http://mountabbeydale.com/index.htm > >> > Sent from Mail for Windows 10> >> > From: Bill Gray pluto@... [mpml]> > Sent: 02 June 2018 16:46> > To: Peter Birtwhistle; neo_followup@yahoogroups.com ; MPML> > Subject: Re: {MPML} Re: [neo_followup] Further on ZLAF9B2> >> >> > Hi Peter,> >> > It's tricky, but possible, to get non-impacting solutions.> > I'm not quite ready to say it's an impactor, and it now seems> > unlikely we'll see follow-up data (except in the form of infrasound> > or satellite detections or somebody saying, "Wow, that was a big> > fireball!")> >> > JPL's Scout system has caught the new data and produced an update,> > with a 30% chance of impact :> >> > https://cneos.jpl.nasa.gov/scout/#/object/ZLAF9B2 > >> > I'm getting a near-certain impact, either a few minutes ago> > (toward the east end of the plot) or in a couple of hours (west end> > of the plot) :> >> > https://projectpluto.com/temp/z.png > >> > Still looking into the cause of the difference, but it'll probably> > come down to differences in uncertainties assumed in the data. (Insert> > here my usual rant about the desirability of astrometric uncertainties> > so that the Scout folks and I don't have to make guesses about how> > good the data are.)> >> > -- Bill> >> > On 2018-06-02 10:26, Peter Birtwhistle peter@... [mpml] wrote:> >> Hi Bill,> >>> >> What would you give for the chance of this one surviving perigee? All of> >> the solutions I get with the revised astrometry look like it won't, but> >> you're *much* better at this stuff than I am!> >>> >> Peter> >> J95> >>> >> On 02/06/2018 13:30, Bill Gray pluto@... [neo_followup] wrote:> >>>> >>> Hello all,> >>>> >>> Alex Gibbs at CSS has re-measured the first few discovery images and> >>> was able to get a position from a previously unmeasured image. So this> >>> replaces the first three positions and adds a fourth. It causes enough> >>> of a change in the situation that I'd recommend using the following for> >>> your ephems. Cut and paste into> >>>> >>> https://www.projectpluto.com/fo.htm > >>>> >>> and do the usual setting of your observatory code, time span, etc.,> >>> and you'll get ephems. That ought to cover us, at least until NEOCP> >>> updates. (At which point, I don't know if NEOCP will include geocentric> >>> perturbations, so I'd still recommend checking with this astrometry and> >>> Find_Orb.)> >>>> >>> For some reason, the on-line Find_Orb isn't providing uncertainties.> >>> But they're already almost two degrees; if it wasn't such a bright object,> >>> we'd be in serious trouble. Still a long shot on such short notice...> >>>> >>> -- Bill> >>>> >>> ZLAF9B2 C2018 06 02.34330 16 11 10.34 -11 19 34.7 G96> >>> ZLAF9B2 C2018 06 02.34851 16 10 59.30 -11 20 21.6 18.2 G G96> >>> ZLAF9B2 C2018 06 02.35373 16 10 48.15 -11 21 08.9 18.3 G G96> >>> ZLAF9B2 C2018 06 02.35895 16 10 36.57 -11 21 57.6 18.0 G G96> >>> ZLAF9B2 C2018 06 02.39785 16 09 02.60 -11 28 26.0 17.5 GUNEOCPI52> >>> ZLAF9B2 C2018 06 02.39804 16 09 02.13 -11 28 28.1 17.2 GUNEOCPI52> >>> ZLAF9B2 C2018 06 02.39822 16 09 01.62 -11 28 30.1 17.5 GUNEOCPI52> >>> ZLAF9B2 C2018 06 02.39840 16 09 01.15 -11 28 31.8 17.7 GUNEOCPI52> >>> ZLAF9B2 C2018 06 02.40223 16 08 51.04 -11 29 13.6 17.7 GUNEOCPG96> >>> ZLAF9B2 C2018 06 02.40233 16 08 50.78 -11 29 15.1 17.9 GUNEOCPG96> >>> ZLAF9B2 C2018 06 02.40242 16 08 50.58 -11 29 16.1 17.8 GUNEOCPG96> >>> ZLAF9B2 C2018 06 02.40251 16 08 50.28 -11 29 16.8 17.8 GUNEOCPG96> >>>> >>>> >>> >>> >>> >> ------------------------------------> >> Posted by: Peter Birtwhistle < peter@... > >> ------------------------------------> >>> >> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~> >>> >> Posts to this list or information found within may be freely used, with the> stipulation that MPML and the originating author are cited as the source of the> information.> >> ------------------------------------> >>> >> Yahoo Groups Links> >>> >>> >>> >> >> >> >> > [Non-text portions of this message have been removed]> >> >> >> > ------------------------------------> > Posted by: AlanCahill < neoprog@... > > ------------------------------------> >> > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~> >> > Posts to this list or information found within may be freely used, with the> stipulation that MPML and the originating author are cited as the source of the> information.> > ------------------------------------> >> > Yahoo Groups Links> >> >> > </s> A magnified view of folio 16v shows the use of a dot as a placeholder on the bottom line.

The concept of zero as a number was revolutionary in mathematics. Historians have long known the idea came from India, but its exact origins remain murky.

Now, the oldest Indian reference to the digit zero has been identified, in a manuscript dating back to the third or fourth century, scientists at the University of Oxford in England announced.

The University of Oxford's Bodleian Libraries has had the famous ancient Indian scroll, the Bakhshali manuscript, in its collection since 1902. A farmer dug up the text from a field in 1881 in the village of Bakhshali, near Peshawar in what is today Pakistan. It consists of 70 leaves of birch bark and contains hundreds of zeros in the form of dots. [Images: The World's 11 Most Beautiful Calculations]

These dots were not zeros like we think of the numeral today. Before zero came to be known as a number in its own right, it was used as a placeholder digit for building larger numbers (as the zero in 101 is doing). Other, more ancient cultures used similar placeholders, such as the Mayans, who used the symbol of a shell, and the Babylonians, who used a double wedge.

The placeholder zero in the Bakhshali manuscript is still "exciting" Marcus du Sautoy, a professor of mathematics at the University of Oxford, said in a statement, because it is "the seed from which the concept of zero as a number in its own right emerged some centuries later, something many regard as one of the of the great moments in the history of mathematics."

The concept of zero as the number representing absolute nothingness paved the way for algebra, calculus and computer science. The first text to discuss zero in the numerical sense is the Indian astronomer Brahmagupta's work "Brahmasphutasiddhanta," which was written in A.D. 628.

Previously, researchers had tried to determine the age of the Bakhshali manuscript by looking at its style of writing and language. A recent Japanese study concluded that the text was likely written between the eighth and the 12th centuries.

The study from Oxford used radiocarbon dating, a method for measuring the content of carbon isotopes in organic material to determine its age (an isotope is a variation of an element that has a different number of neutrons in its nucleus). The results produced a further complication: The Bakhshali manuscript might not be a single text but several texts.

The carbon dating resulted in three different dates for different parts of the manuscript. The oldest part dated to A.D. 224-383, but two other parts dated to A.D. 680-779 and A.D. 885-993.

"It is possible that the Bakhshali manuscript is made up of more than one text," one of the researchers, Camillo Formigatti, a Sanskrit librarian at the Bodleian Libraries, wrote in statement from Oxford. "More research is needed to better understand what the manuscript consists of." </s> According to Times of India, the symbol "0" is a familiar sight, but its origins are far from certain. A recent batch of carbon dating is causing the history of mathematics to be rewritten, as it has discovered zeros dating back to a period 500 years before previously seen.

The numbers appear in an ancient Indian text called the Bakhshali manuscript, which consists of 70 leaves of birch bark, filled with mathematics and text in the form of Sanskrit.

"It seems to be a training manual for Buddhist monks," says Marcus du Sautoy at the University of Oxford.The manuscript was first discovered by a local farmer in 1881, and was named after the village it was found in, in what is now Pakistan. It's been housed by the University of Oxford's Bodleian Library since 1902.

Now, the manuscript has been carbon dated -and this has immediately upturned commonly held beliefs. It was originally thought that the manuscript was from the 9th century, but the dating methods revealed that the oldest pages are from somewhere between 224 AD and 383 AD. This means that the manuscript predates a 9th century inscription of zero on the wall of a temple in Gwalior, India, which was previously considered to be the oldest recorded example of a zero.

Across the text there are hundreds of zeros denoted using a dot. It's this dot that later evolved to be the symbol with a hole in the middle that we know today. The dot was originally used as a placeholder, like how "0" is used in the number 505 to denote that there are no tens, but was not yet a number in its own right. The use of zero as a placeholder appeared in several different ancient cultures, such as the ancient Mayans and Babylonians. But only the Indian dot would eventually go on to gain true number status, first described in 628 AD by the Indian astronomer and mathematician Brahmagupta.

"Some of these ideas that we take for granted had to be dreamt up. Numbers were there to count things, so if there is nothing there why would you need a number?" says du Sautoy. The concept of zero, initially banned as heresy, was eventually allowed for the development of calculus, and underpins the digital age. "The whole of modern technology is built on the idea of something and nothing," he says. </s> A new carbon dating study commissioned by the University of Oxford’s Bodleian Libraries has revealed that the zero originated in the third or fourth century AD, 500 years before originally thought. Researchers found that the ancient Indian Bakhshali manuscript, which contains hundreds of zeroes, dates from the third or fourth century AD, the Bodleian Libraries said in a report on Thursday.

The new findings mean that the zero predates the ninth-century inscription of the digit found on the wall of a temple in Gwalior in Madhya Pradesh, earlier thought to be the oldest recorded use of the zero. In the Bakhshali manuscript, found near Taxila, the zero is in the form of a dot, used as a placeholder – meaning that it was used to indicate orders of magnitude in a number system.

The ancient Babylonians and Mayans had also used the zero as a placeholder, but the Bodleian Libraries report says that it was in India that the zero evolved from a dot into a circle. Secondly, it was only in India that the zero developed into a number used in mathematical equations.

‘Today we take it for granted that the concept of zero is used across the globe and is a key building block of the digital world,” Marcus du Sautoy, professor of Mathematics at the University of Oxford said. “But the creation of zero as a number in its own right, which evolved from the placeholder dot symbol found in the Bakhshali manuscript, was one of the greatest breakthroughs in the history of mathematics. We now know that it was as early as the third century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world.”

The report says that the first document which discusses the zero as a number is the Brahmasphutasiddhanta, written by the Indian mathematician and astronomer Brahmagupta in 628 AD. The Bakhshali manuscript was found in 1881, buried in a field in a village called Bakhshali near Peshawar.
The Great Internet Mersenne Prime Search announces the discovery of a new Mersenne prime, 282,589,933-1. It has 24,862,048 decimal digits, which surpasses the previous record by over 1.5 million digits.