umasundresh

Bertrand’s Postulate

For every number greater than 1, there is at least one prime number between the number and its double.

Bertrand’s postulate states that there is at least one prime number p, such that n < p < 2n.

Pictorial representation

This Postulate was first proposed by Bertrand in 1845.

However, Bertrand did check that his conjecture was true up to 3 million.

It was first proved in 1850 by Chebyshev so is also called the Bertrand-Chebyshev Theorem.

Chebyshev on a 2021 stamp of Russia

The Indian Mathematician Ramanujan, who was not aware of Chebyshev’s proof, came up with an easier proof on 1919.

In 1932, a Hungarian Mathematician, Paul Erdos, came with another different proof.

Bertrand Russell

Bertrand Russell (18 – 05 – 1872 to 02 – 02 -1970), a famous British mathematician.

In his autobiography he mentioned

It was my desire to know more about Mathematics that kept me away from suicide

Bertrand Russell
Bertrand Russell on 1972 stamp of India

Goldbach’s Conjecture

Goldbach’s conjecture is one of the oldest unsolved problems in mathematics.


Any even number greater than 2 can be written as the sum of two prime number.

Every odd whole number greater than 5 can be written as the sum of three primes. 

Goldbach’s conjectures

Goldbach, a Prussian mathematician(1690-1764)

On 7 June 1742, Goldbach wrote a letter to the mathematician Euler in which he proposed the conjectures he found.

Euler responded back on 30 June 1742 as

Every integer greater than 2 is a sum of two primes, I regard this as a completely certain theorem, although I cannot prove it.

Euler

Though the Goldbach’s conjecture looks simple to understand, it has not yet been proved.

In the modern times, the conjectures proposed by Goldbach is identified as weak or strong Goldbach conjecture.

STRONG GOLDBACH CONJECTURE

Any even whole number greater than 2 can be written as the sum of two prime number.

WEAK GOLDBACH CONJECTURE

Every odd whole number greater than 5 can be written as the sum of three primes. 

In 2013, Harold Helfgott, a Peruvian mathematician released two papers claiming the proof of Goldbach weak conjecture and The proof was accepted for publication in the Annals of mathematics series in 2015, and has been undergoing further review and revisions.

In March 2000 the publishers of the book ‘Uncle Petros and Goldbach’s conjecture (Bloomberg in the USA and Faber and Faber in the UK) offered a prize of one million dollars for anyone who could prove the Goldbach’s conjecture

Any even whole number greater than 2 can be written as the sum of two prime number.

The prize was kept open for two years, but nobody claimed it.

Co-prime numbers

A set of numbers which has 1 as the only common factor is called as co-prime.

We require at least two numbers to check whether they are co-prime or not, they are also called as co-prime pair.

The numbers need not be prime numbers to form a co-prime.

Finding whether any set of numbers are co-prime is very easy ✌.

Finding GCF gives the answer

If their GCF is 1, then that is co-prime.

GCF or HCF of the set of numbers should be 1.

Properties of Co-prime numbers

How to check Co-Prime numbers?

Happy learning!!!

Odd(number) Fact

A cool fact about odd numbers.

2520 – Amazing fact about this number.

2520

Dudeney Number

Henry Dudeney, a self taught Mathematician known for his puzzles, first noted the existence of these numbers while framing one of his puzzles.

What’s so special about these numbers?

What is the pattern followed behind the construction of these numbers?

Yes! There is a very interesting pattern behind these numbers.

Let’s check that pattern in the following video.

Dudeney numbers

The magic number 1089

This math trick helps the kids think about the patterns behind the calculation and their amazing fixed answer.

Mastering this concept will make them believe that they are a tricky mathe-magician.

The following video will explain about the math trick behind the magic number 1089.

The mathematical proof of the above trick is as follows:

Narcissistic number

Interesting name, isn’t it?

How can a number be narcissistic?

☻When it focuses too much on itself☺.

It will represent itself even after some manipulation of its digits.

“A number is said to be narcissistic if the sum of its own digits each raised to the power of the number of digits is equal to itself”

For example:

153=13 + 53 + 33 = 153.

These numbers are also called as Armstrong numbers or plus perfect numbers.

The following video has some details about this…

Narcissistic number

Blaise Pascal

Yesterday was the birth anniversary of the famous French Mathematician Blaise Pascal(18-6-1623 to 19 -8-1662). He is a child prodigy with no formal education.

He invented the mechanical calculator at a very young age.

He is the first person who proposed the idea of public transportation in 1662 in France. He introduced the seven horse drawn carriage routes for the public. They are called as the “Five-Penny Coaches,” or “Carosses à Cinq Sous”.

In science, his focus was mainly on fluid dynamics.

The following video explains his other achievements

Blaise Pascal