Tag: Numbers

Most Precise Measurement Of The Proton’s Mass

What is the weight of a proton? Scientists from Germany and Japan have made an important step toward better understanding this fundamental constant.

By means of precision measurements on a single proton, they were able to improve the precision by a factor of three and also correct the existing value.

To determine the mass of a single proton more accurately, the group of physicists from the Max Planck Institute for Nuclear Physics in Heidelberg and RIKEN in Japan performed an important high-precision measurement.

In a greatly advanced Penning trap system, designed by Sven Sturm and Klaus Blaum from MPI-K, using ultra-sensitive single particle detectors that were partly developed by RIKEN’s Ulmer Fundamental Symmetries Laboratory.

The proton is the nucleus of the hydrogen atom and one of the basic building blocks of all other atomic nuclei. Therefore, the proton’s mass is an important parameter in atomic physics: it is one of the factors that affect how the electrons move around the atomic nucleus.

This is reflected in the spectra, i.e., the light colours (wavelengths) that atoms can absorb and emit again. By comparing these wavelengths with theoretical predictions, it is possible to test fundamental physical theories.

Further, precise comparisons of the masses of the proton and the antiproton may help in the search for the crucial difference – besides the reversed sign of the charge – between matter and antimatter.

Penning traps are well-proven as suitable “scales” for ions. In such a trap, it is possible to confine, nearly indefinitely, single charged particles such as a proton, for example, by means of electric and magnetic fields.

Inside the trap, the trapped particle performs a characteristic periodic motion at a certain oscillation frequency. This frequency can be measured and the mass of the particle calculated from it.

In order to reach the targeted high precision, an elaborate measurement technique was required.

The carbon isotope 12C with a mass of 12 atomic mass units is defined as the mass standard for atoms. “We directly used it for comparison,” says Sven Sturm.

First we stored each one proton and one carbon ion (12C6+) in separate compartments of our Penning trap apparatus, then transported each of the two ions into the central measurement compartment and measured its motion.

From the ratio of the two measured values the group obtained the proton’s mass directly in atomic units. The measurement compartment was equipped with specifically developed purpose-built electronics.

Andreas Mooser of RIKEN’s Fundamental Symmetries Laboratory explains its function: “It allowed us to measure the proton under identical conditions as the carbon ion despite its about 12-fold lower mass and 6-fold smaller charge.”

The resulting mass of the proton, determined to be 1.007276466583(15)(29) atomic mass units, is three times more precise than the presently accepted value.

The numbers in parentheses refer to the statistical and systematic uncertainties, respectively.

Intriguingly, the new value is significantly smaller than the current standard value.

Measurements by other authors yielded discrepancies with respect to the mass of the tritium atom, the heaviest hydrogen isotope (T = 3H), and the mass of light helium (3He) compared to the “semiheavy” hydrogen molecule HD (D = 2H, deuterium, heavy hydrogen).

Our result contributes to solving this puzzle, since it corrects the proton’s mass in the proper direction,” says Klaus Blaum.

Florian Köhler-Langes of MPIK explains how the researchers intend to further improve the precision of their measurement: “In the future, we will store a third ion in our trap tower. By simultaneously measuring the motion of this reference ion, we will be able to eliminate the uncertainty originating from fluctuations of the magnetic field.”

The work was published in Physical Review Letters.

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The Largest Prime Number Was Discovered By A FedEx Employee

A FedEx employee in Tennessee has discovered the largest known prime number.

Germantown, Tenn., resident John Pace found the number through his volunteer work with the Great Internet Mersenne Prime Search (GIMPS), a project that crowd sources computing power to search for a subset of prime numbers called Mersenne primes.

Like a normal prime number, these can only be divided by themselves and one. What sets them apart is that they can all be expressed as the number 2 raised to a given power minus one.

The newly discovered Mersenne prime, called M77232917, can be expressed as 2 to the 77,232,917 power minus one. It’s the 50th Mersenne prime to be discovered and it’s more than 23 million digits long.

Pace might be the only person in history who went into math for the money.

He told NPR, “There was a $100,000 prize attached to finding the first prime that had a 10 million digit result, and I was like, ‘Well you know, I’ve got as much chance as anybody else.’

He has been participating in the program for 14 years and this is his first discovery.

The previous longest-known prime number was discovered in January of 2016 at the University of Central Missouri. It contains 22 million digits and is also a Mersenne prime.

Large prime numbers are important for the future of computing and cyber security, and the search is already on for larger numbers.

The Electronic Frontier Foundation is offering a prize of $150,000 for finding the first prime number with one hundred million digits and $250,000 for finding the first prime with one billion digits.

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Largest Known Prime Number Discovered With Over 23 Million Digits

A collaborative computational effort has uncovered the longest known prime number.

At over 23 million digits long, the new number has been given the name M77232917 for short.

Prime numbers are divisible only by themselves and one, and the search for ever-larger primes has long occupied maths enthusiasts.

However, the search requires complicated computer software and collaboration as the numbers get increasingly hard to find.

M77232917 was discovered on a computer belonging to Jonathan Pace, an electrical engineer from Tennessee who has been searching for big primes for 14 years.

Mr Pace discovered the new number as part of the Great Internet Mersenne Prime Search (GIMPS), a project started in 1996 to hunt for these massive numbers.

Mersenne primes – named after the 17th century French monk Marin Mersenne who studied them – are calculated by multiplying together many twos and then subtracting one.

Six days of non-stop computing in which 77,232,917 twos were multiplied together resulted in the latest discovery.

The number is the 50th Mersenne prime to be discovered, and the 16th to be discovered by the GIMPS project.

It is nearly one million digits longer than the previous record holder, which was identified as part of the same project at the beginning of 2016.

Mersenne primes are a particular focus for prime aficionados because there is a relatively straightforward way to check whether a number is one or not.

Nevertheless, the new prime has to be verified using four different computer programs on four different computers.

The process also relies on thousands of volunteers sifting through millions of non-prime candidates before the lucky individual chances upon their target.

Professor Caldwell runs an authoritative website on the largest prime numbers, with a focus on the history of Mersenne primes.

He emphasised the pure excitement that searching for prime numbers brings, describing the latest discovery as “a museum piece as opposed to something that industry would use”.

Besides the thrill of discovery, Mr Pace will receive a $3,000 (£2,211) GIMPS research discovery award.

GIMPS uses the power of thousands of ordinary computers to search for elusive primes, and the team behind it state that anybody with a reasonably powerful PC can download the necessary software and become a “big prime hunter”.

The next Mersenne prime discovery could be smaller or larger than the existing record holder, but the big target for the GIMPS team is to find a 100 million digit prime number.

The person who discovers such a number will be awarded $150,000 by the Electronic Frontier Foundation for their efforts.

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The 500-Page Proof That Only One Mathematician Can Understand

Nearly four years after Shinichi Mochizuki unveiled an imposing set of papers that could revolutionize the theory of numbers, other mathematicians have yet to understand his work or agree on its validity.

Although they have made modest progress.

Some four dozen mathematicians converged last week for a rare opportunity to hear Mochizuki present his own work at a conference on his home turf, Kyoto University’s Research Institute for Mathematical Sciences (RIMS).

Mochizuki is “less isolated than he was before the process got started”, says Kiran Kedlaya, a number theorist at the University of California, San Diego.

Although at first Mochizuki’s papers, which stretch over more than 500 pages, seemed like an impenetrable jungle of formulae.

Experts have slowly discerned a strategy in the proof that the papers describe, and have been able to zero in on particular passages that seem crucial, he says.

Mochizuki’s theorem aims to prove the important abc conjecture, which dates back to 1985 and relates to prime numbers — whole numbers that cannot be evenly divided by any smaller number except by 1.

The conjecture comes in a number of different forms, but explains how the primes that divide two numbers, a and b, are related to those that divide their sum, c.

If Mochizuki’s proof is correct, it would have repercussions across the entire field, says Dimitrov.

When you work in number theory, you cannot ignore the abc conjecture,” he says.

This is why all number theorists eagerly wanted to know about Mochizuki’s approach.”

For example, Dimitrov showed in January how, assuming the correctness of Mochizuki’s proof, one might be able to derive many other important results, including a completely independent proof of the celebrated Fermat’s last theorem.

But the purported proof, which Mochizuki first posted on his webpage in August 2012, builds on more than a decade of previous work in which Mochizuki worked in virtual isolation and developed a novel and extremely abstract branch of mathematics.

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Pass it on: New Scientist