Abstract1

The ‘new’ largest known Prime Number

Great Internet Mersenne Prime Search (GIMPS) group has reported an all new Mersenne Prime Number (a prime number of type $2^P-1$) which is, now officially the largest prime number ever discovered. This number is valued to a whopping $2^{74207281}-1$ and contains 22,338,618 digits. It is quoted as M747207281 and is almost 5 million digits longer than the previous record holding prime number M57885161. It took non-stop calculations of an i7 computer for 31 days to prove the primality of the number. A…

Solving Integral Equations (4) : Integral Equations into Differential Equations

Introduction In earlier parts we discussed about the basics of integral equations and how they can be derived from ordinary differential equations. In second part, we also solved a linear integral equation using trial method. Now we are in a situation from where main job of solving Integral Equations can be started. But before we go ahead to that mission, it will be better to learn how can integral equations be converted into differential equations. Integral Equation ⇔ Differential Equation The method of converting…

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Test your counting skills with Branifyd game for Android

Without basic operations of counting, like Addition, Subtraction, Multiplication and Division, it is not possible to imagine math problems. Counting is the base of human life. A student, whether he’s a math major or not, must be good at counting numbers.  The counting ability builds from experience and is definitely a time taking process.   Larger you have given time on counting, better you become. This is why some students have better counting skills than other and this is also,…

Painted Diary

This Prime Generating Product generates successive prime factors

Any integer greater than 1 is called a prime number if and only if its positive factors are 1 and the number p itself. The basic ideology involved in this post is flawed and the post has now been moved to Archives. - The Editor Prime Generating Formulas We all know how hard it is to predict a formula for prime numbers! They have extremely uncertain pattern at various number ranges. Some prime numbers may have difference of hundreds, while few others are as…

Pen Paper And PHP

A Possible Proof of Collatz Conjecture

Our reader Eswar Chellappa has sent his work on the solution of '3X+1' problem, also called Collatz Conjecture. He had been working on the proof of Collatz Conjecture off and on for almost ten years. The Collatz Conjecture can be quoted as follow: Let $\phi : \mathbb{N} \to \mathbb{N}^+$ be a function defined  such that: $$\phi(x):= \begin{cases} \frac{x}{2}, & \text{if } x \text{ is even } \\ 3x+1, & \text{ if } x \text{ is odd} \end{cases}$$ Then the iterates of…

Mathoverflow

8 big online communities a math major should join

Online communities are the groups of web savvy individuals who share communal interests. A community can be developed with just a single topic or by a bunch of philosophies. A better community binds its members through substantial debates. Mathematics is a very popular communal interest and there are hundreds of online communities formed in both Q&A and debate styles. Some mathematical communities are so immense that they serve two or three discussions every minute. If you are a math student,…

Unlocked Lock

New Math Series: Selected Topics in Functional Analysis

This series of study notes is aimed for post-graduate (M.A/M.Sc.) students of Indian & international universities. The study of functional analysis can be started after basic topology and set theory courses. In this introductory article we will start with some elementary yet important definitions and notations from analysis. We will finish this article with the definition of Norm & Normed Linear spaces derivedfrom the notions of linear spaces. An elementary treatise of examples and their completeness of Normed (linear) Spaces will…

Meet the Math Blogger : Josh Young from Mathematical Mischief

Every mathematics student is in his own a special case — having his own qualities and snags. A math blogger is even more special.  He is more than just a mathematician or just a blogger. A math blogger is an entertainer… a magician, who devises techniques of making math more readable and even more interesting. There are hundreds of such mathemagicians blogging about thoughtful and fun-aspects of mathematics. In this series of talks, called “Meet the Math Blogger“, I’ll be…

Mobile Number Is Prime Number

My mobile number is a prime number

My personal mobile number 9565804301 is a prime number. What is a prime number? Any integer p greater than 1 is called a prime number if and only if its positive factors are 1 and the number p itself. In other words, the natural numbers which are completely divisible by 1 and themselves only and have no other factors, are called prime numbers. 2 ,3 ,5 ,7 ,11 ,13 ,17 , 19 ,23 ,29 …  etc. are prime numbers [or just Primes]. The numbers greater than 1, which are not prime are called Composite numbers.  …

10 Fun puzzles to enjoy today

1st April is a day of fun, humor and enjoyment. Even though, I have lot of fun puzzles on this blog, these ten are totally meant for today. Enjoy! PUZZLES 1. If you are in a dark room with a candle, a wood stove and a gas lamp. You only have one matchstick in the matchbox, so what do you light first? 2. If the question you answered before you answered the question you answered after you answered the question you answered…

Abel Prize Laureate

Abel Prize for 2014 to Yakov Sinai

Mathematical Physicist Yakov Gregory Sinai, (b. 21st September 1935, 78 years old) has been awarded the prestigious Abel Prize for 2014 by the Norwegian Academy of Science and Letters (NASL). The President of the NASL, Nils C. Stenseth, announced the winner of the 2014 Abel Prize at the Academy in Oslo on 26 March 2014. The Abel Prize recognizes contributions of extraordinary depth and influence to the mathematical sciences and has been awarded annually since 2003. It carries a cash award…