Something About Prime Numbers

This is a part of the article i found really interesting.

Back in August an new algorithm was announced for determining if large numbers were prime. I wondered if this panned out. I further wondered what the implications were for cryptographic systems that depend on the difficulty of factoring large numbers into primes.

A team of Indian scientists has developed a solution for an ancient and important problem — how to find out whether a number is a prime or not. Professor Manindra Agrawal, with his students Mr Neeraj Kayal and Mr Nitin Saxena from the Indian Institute of Technology in Kanpur, came up with a computer algorithm that solves the problem. The students have only recently completed their undergraduate degrees. Their result was announced on August 4 and published on their website on August 7. Within 24 hours, more than 30,000 people worldwide had downloaded the paper.

"The strength of this process is it says a number is prime if and only if it is prime. There is no percentage margin of error," said triple j's Mr Adam Spencer, a mathematician by training. The algorithm, or set of instructions, is unique because it is 100 per cent accurate — something that has not been achieved before. Prime numbers are divisible only by themselves and the number one. They are extremely valuable in computing science and mathematics.

Encryption of information transferred over the Internet, for example, is achieved in 'packages' of large semi-prime numbers (which are divisible only by two prime numbers). These packages are known as RSA numbers, and unless the receiver knows which prime numbers are used to make the RSA number, they will not be able to decode the information. "Any developments in terms of determining primes, or calculating primes, or unravelling if things are semi-prime, will have implications for cryptography because the basis of cryptography is knowing massive prime numbers," Mr Spencer explained. But until now there has not been an efficient method of determining whether a number is prime or not — a dilemma known as the primality testing problem.

Existing computer programs are able to estimate prime numbers, but they carry a small degree of inaccuracy — either failing to find a prime number, or coming up with a number that actually isn't prime. While the new algorithm is a polynomial time algorithm — one that is efficient in the time it takes to compute — current methods are faster because they use less steps.The Indian researchers have indicated that their next challenge will be to reduce the number of steps.

The 10 largest prime numbers known are Mersenne primes, named after the 17th-Century French monk Marin Mersenne. He established that (2^p)–1 (that is, two to the power of 'p', minus one — where p is a prime number) is sometimes prime. This is the form of most of the large primes discovered, said Mr Spencer. "These Mersenne numbers aren't always prime," he explained. "But with Mersenne numbers it's particularly easy to test if they are prime or not." By contrast, the process to determine if any random number is prime or not is extremely complicated. The new algorithm offers a foolproof way of doing this. The algorithm does not, however, generate prime numbers — and to date there is no way to do this.

"If someone was to develop a program that was able to factorise numbers, the whole security process of data would collapse," said Mr Spencer.

code4bill

Today I was eliminated from the code4bill contest. I reached round 3 but couldnt qualify for the next stage. This was what i aimed for... Had i cleared this round, i would have then been thrown out of the competition as i was not eligible for it from the start.. It was only for 3rd and 4th year students.

The concept of Black Holes

Astronomically, Black Holes are heavenly bodies with mass so high, that they are capable of creating a gravitational field so strong that even light cannot escape it. Thus it is very difficult to observe black holes coz anything that goes towards them, is sucked into them forever.

In my life, I have seen a lot of black holes. They are not rare, but abundantly present all around. Well that’s coz I have a little different definition of black holes from NASA or wikipedia. I refer those people as black holes who somehow have the habit of borrowing stuff, but somehow seem to forget to return it. Anything that goes to these ‘black holes’ have little or approximately zero probability of coming back to the mother ship.

Due to some weird reason (the research is going on), these black holes assume that anything that’s coming their way should not be returned to their home planet. Every object i.e. matter that is directed towards these black holes is sucked into them by an unknown type of force. The only known characteristics of the force are as follows

The origin of the force is need.
The force is attractive in nature to every kind of material known to mankind.
The force makes the black hole system ‘memoryless’ i.e. the whole black hole system has no record of the instances when the force is on its peak.