Saturday, August 13, 2016

Largest Known Prime Number Discovered in a University of Central Missouri Computer

It may be seen only as a mathematical curiosity to most of us, but did you know that very large prime numbers are indispensable in maintaining effective cyber security?

By: Ringo Bones 

Previously seen as a mere mathematical curiosity – and it still is by most of the population – but prime numbers – such as two, three, five and seven – numbers that are divisible only by themselves and one, play a vital role in computer data encryption. The latest prime number discovered so far back in January 20, 2016 is more than 22-million digits long – 22,338,618 digits long to be exact - five million digits longer than the previously discovered largest known prime number. Prime numbers this large could prove useful to computing in the future – which is sooner than you might think given the current rapidity of advances in hardware and software. 

The new prime number was found as part of the “endless mathematical quest” called the Great Internet Mersenne Prime Search or GIMPS, a global quest to find a particular type of large prime numbers. Mersenne Primes are named after a French monk, Marin Mersenne, who studied them in the 17th Century during his spare time. Given that modern programmable digital computers processes data in binary code, they can be configured to hunt for Mersenne Prime Numbers by multiplying two by itself a large number of times, then taking away one. It is a relatively manageable calculation for today’s computers, but not every result is a prime number. This year’s newly discovered prime number is written as 2^74,207,281-1, which denotes the number two, multiplied by itself 74,207,280 times with one subtracted afterwards. Since it began 29 years ago, the GIMPS project has calculated the 15 largest Mersenne Prime Numbers and it is possible that there could still be an infinite number of them to discover.  

Very large prime numbers are important in computer encryption and help make sure that online banking, shopping and private messaging services are secure, but current encryption typically use prime numbers that are only hundreds of digits long – not millions. But given our increasing reliance on computers for online commerce and private messaging, the search for very large prime numbers can be very important to maintain encryption with ever increasing processing power – although mathematicians involved in the GIMPS project admitted in a statement that this year’s newly discovered prime number is “too large to currently be of practical value”. 

However, searching for large prime numbers is intensive work for computer processors and can have unexpected benefits. “One prime project discovered that there was a problem in some computer processors that only showed up in certain circumstances.” said Dr. Steven Murdoch, cybersecurity expert at University College London. This year’s new large prime number – the 49th known Mersenne Prime Number, was discovered by Dr. Curtis Cooper at the University of Central Missouri. Although computers do most of the hard work, very large prime numbers are said to be discovered only after when a human operator takes note of the result. 

Sunday, January 31, 2016

Ancient Babylonians: First To Use Sophisticated Geometry?

Previously known for starting an order of astrologer-priests, are the Ancient Babylonians are also the first ones to use sophisticated geometry? 

By: Ringo Bones

Before the recent research findings were published back in January 29, 2016, Ancient Babylonians were more famous for establishing the first order of astrologer-priests that would later evolve into what we know as the science of astronomy. But that all changed when evidence were uncovered that Ancient Babylonians were using a branch of geometry that only got widespread use in the 14th Century. The new study is published in the journal Science. Its author, Prof. Mathieu Ossendrijver from the Humboldt University of Berlin, Germany said: “I wasn’t expecting this. It is completely fundamental to physics and all branches of science use this method.” The study suggests that sophisticated geometry – the branch of mathematics that deals with shapes – was being used at least 1,400 years earlier than previously thought. 

The possibility that Ancient Babylonians were using geometrical calculations to track the planet Jupiter across the night sky entered the realm of plausibility after Prof. Ossendrijver examined five Babylonian tablets that were excavated in the 19th Century and which are now held in the British Museum’s archives. The script reveals that the Babylonians were using four-sided shapes, called trapezoids, to calculate when Jupiter would appear in the night sky and also the speed and distance that it traveled. “This figure – a rectangle with a slanted top – describes how the velocity of a planet, which is Jupiter, changes with time,” he said. “We have a figure where one axis, the horizontal side, represents time, and the other axis, the vertical side, represents velocity.” “The area of the trapezoid gives you the distance traveled by Jupiter along its orbit.” “What is so special is that this type of graph is unknown from antiquity – so making figures of motion in this rather abstract space of velocity against time – this is something very, very new.” It has been previously thought that complex geometry was first used by scholars in Oxford and Paris in Medieval times.    

The Ancient Babylonians once lived in what is now Iraq and Syria. The civilization emerged in about 1,800 BC. Clay tablets engraved in their Cuneiform writing system have already shown these people were advanced in astronomy. “They wrote reports about what they saw in the sky,” Prof. Ossendrijver told the BBC World Service’s Science In Action programme. “And they did this over a very long period of time, over centuries,” he says.