Numbers – The Basic Introduction

If mathematics was a language, logic was the grammar, numbers should have been the alphabet. There are many types of numbers we use in mathematics, but at a broader aspect we may categorize them in two categories: 1. Countable Numbers 2. Uncountable Numbers The numbers which can be counted in nature are called Countable Numbers and the numbers which can not be counted are called Uncountable Numbers. Well, this is not the correct way to classify the bunch of types…

Fermat Numbers

Fermat Number, a class of numbers, is an integer of the form $ F_n=2^{2^n} +1 \ \ n \ge 0$ . For example: Putting $ n := 0,1,2 \ldots$ in $ F_n=2^{2^n}$ we get $ F_0=3$ , $ F_1=5$ , $ F_2=17$ , $ F_3=257$ etc. Fermat observed that all the integers $ F_0, F_1, F_2, F_3, \ldots$ were prime numbers and announced that $ F_n$ is a prime for each natural value of $ n$ . In writing to…

Largest Prime Numbers

What is a Prime Number? An integer, say $ p $ , [ $ \ne {0} $ & $ \ne { \pm{1}} $ ] is said to be a prime integer iff its only factors (or divisors) are $ \pm{1} $ & $ \pm{p} $ . As? Few easy examples are: $ \pm{2}, \pm{3}, \pm{5}, \pm{7}, \pm{11}, \pm{13} $ .......etc. This list goes up to infinity & mathematicians are trying to find the larger one than the largest, because primes…