November 18, 2016 Friday
Bedtime Story
Prime Obsession
Nothing has obsessed the mathematicians more than the prime
numbers for ages and centuries.
Even the number of books on popular mathematics that deal with the
primes are hard to count.
Primes have been the focus and subject of so many conjectures and
hypothesis, most prominent being the Riemann hypothesis and Goldbach’s
conjecture.
The definition of prime number quite a simple one and does not
seem very remarkable at first glance.
Prime number is a natural number (positive integers) that has
exactly 2 divisors, 1 and itself.
1 is not considered a prime.
All other numbers that are greater than 1 and that are not primes
are called composites.
Why 1 is not considered a prime is yet another interesting story
that has to be narrated in detail.
Why are prime numbers which apparently do not seem to be much
different than an average natural number get so much scrutiny?
For one, the primes form the basis of the most fundamental theorem
of arithmetic that goes as far back as 300 B.C. to the time of that great genius
Euclid.
In his book VII proposition 30, is a statement that is known as
Euclid’s lemma.
A lemma in mathematics is a proposition that has been proved and
is used in turn to build up and prove something even bigger and larger.
Euclid’s lemma states that if a prime p divides the product ab of
2 integers a and b, then p must at least divide one of those integers a and b.
You can take any example, say p = 5 and ab = 2025.
Here a = 25 and b = 81.
Since 2025 is divisible by 5, Euclid’s lemma states that either 25
or 81 or both will be divisible by 5.
In this case 25 is divisible by 5.
In his next proposition 31, Euclid states:
Any composite number is measure by some prime number.
In proposition 32, Euclid states:
Any number is either prime, or is measured by some prime.
These propositions of Euclid in his book VII form the basis of
fundamental theorem of arithmetic.
The fundamental theorem states that every integer that is greater
than 1 is either a prime or is a product of prime numbers and moreover, this
product is unique up to the order of factors.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night and my fellow cousin ape.
Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, may I
suggest this large collection of Kids Songs:
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