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Smell everything with Google Nose!
Just figured Google Nose (beta) in Google Search results, a great new feature which make you smell the things. Like how does a ‘wet dog’ smell and how do the ‘lemons’!
Here is a promotional video of Google Nose (beta) from YouTube, which explains how can you smell things from your device! 
Life After Google Reader
Seems like a false title, should have been “Life after the announcement of death of Google Reader” – whatever, Google Reader is reaching to its end now — people are quickly moving to other RSS feed readers after Google announced the death of the best feed reader service on March 13. I was using this service since 2009 and have read over 20 of thousands of articles through it. As a student, Google Reader meant a lot to me; whether it’s about reading the informative WordPress.com News or going through Terence Tao’s notes: Google Reader was everywhere. Now all the applications which were based Google Reader API, will not be functioning after 1st July, so there was a desperate need of finding a new Feed-Reader for me.
Here are the Google Reader alternatives, which I gave rigorous tries and found useful.
Happy Holi! : The Village Tour
Holi, the festival of colors, was celebrated this year on 27th and 28th of March all over India. I decided to move to my own village, Kasturwa and then to Surya’s Village, Shiv Patti, on this occasion. Here are some images from the events taken with my Nokia device, which I thought were worth sharing.
ENJOY READING! Err… Watching.
Euler’s (Prime to) Prime Generating Equation
The greatest number theorist in mathematical universe, Leonhard Euler had discovered some formulas and relations in number theory, which were based on practices and were correct to limited extent. The prime generating equation by Euler is a binomial which is actually very specific and yields more primes than any other relations out there in number theory. Euler told that the equation 
Let’s see how many primes we can get by using different values of k and x:
| Serial Number | Value of k (prime) | Value of x (from x=0 to x=k-2) | Value of f(x)=(x^2+x)+k | Not a Prime? |
| 1 | 2 | 0 | 2 | |
| 2 | 3 | 0 | 3 | |
| 3 | 1 | 5 | ||
| 4 | 5 | 0 | 5 | |
| 5 | 1 | 7 | ||
| 6 | 2 | 11 | ||
| 7 | 3 | 17 | ||
| 8 | 7 | 0 | 7 | |
| 9 | 1 | 9 | No | |
| 10 | 2 | 13 | ||
| 11 | 3 | 19 | ||
| 12 | 4 | 27 | No | |
| 13 | 5 | 37 | ||
| 14 | 11 | 0 | 11 | |
| 15 | 1 | 13 | ||
| 16 | 2 | 17 | ||
| 17 | 3 | 23 | ||
| 18 | 4 | 31 | ||
| 19 | 5 | 41 | ||
| 20 | 6 | 53 | ||
| 21 | 7 | 67 | ||
| 22 | 8 | 83 | ||
| 23 | 9 | 101 | ||
| 24 | 13 | 0 | 13 | |
| 25 | 1 | 15 | No | |
| 26 | 2 | 19 | ||
| 27 | 3 | 25 | No | |
| 28 | 4 | 33 | No | |
| 29 | 5 | 43 | ||
| 30 | 6 | 55 | No | |
| 31 | 7 | 69 | No | |
| 32 | 8 | 85 | NO | |
| 33 | 9 | 103 | ||
| 34 | 10 | 123 | No | |
| 35 | 11 | 145 | No | |
| 36 | 17 | 0 | 17 | |
| 37 | 1 | 19 | ||
| 38 | 2 | 23 | ||
| 39 | 3 | 29 | ||
| 40 | 4 | 37 | ||
| 41 | 5 | 47 | ||
| 42 | 6 | 59 | ||
| 43 | 7 | 73 | ||
| 44 | 8 | 89 | ||
| 45 | 9 | 107 | ||
| 46 | 10 | 127 | ||
| 47 | 11 | 149 | ||
| 48 | 12 | 173 | ||
| 49 | 13 | 199 | ||
| 50 | 14 | 227 | ||
| 51 | 15 | 257 | ||
| 52 | 19 | 0 | 19 | |
| 53 | 1 | 21 | ||
| 54 | 2 | 25 | No | |
| 55 | 3 | 31 | ||
| 56 | 4 | 39 | No | |
| 57 | 5 | 49 | ||
| 58 | 6 | 61 | ||
| 59 | 7 | 75 | No | |
| 60 | 8 | 91 | No | |
| 61 | 9 | 109 | ||
| 62 | 10 | 129 | No | |
| 63 | 11 | 151 | ||
| 64 | 12 | 175 | No | |
| 65 | 13 | 201 | No | |
| 66 | 14 | 229 | ||
| 67 | 15 | 259 | ||
| 68 | 16 | 291 | ||
| 69 | 17 | 325 | No | |
| 70 | 23 | 0 | 23 | |
| 71 | 1 | 25 | No | |
| 72 | 2 | 29 | ||
| 73 | 3 | 35 | No | |
| 74 | 4 | 43 | ||
| 75 | 5 | 53 | ||
| 76 | 6 | 65 | No | |
| 77 | 7 | 79 | ||
| 78 | 8 | 95 | No | |
| 79 | 9 | 113 | ||
| 80 | 10. | 133 | ||
| 81 | 11 | 155 | No | |
| 82 | 12 | 179 | ||
| 83 | 13 | 205 | No | |
| 84 | 14 | 233 | ||
| 85 | 15 | 263 | ||
| 86 | ||||
| 87 | 16 | 295 | No | |
| 88 | 17 | 329 | ||
| 89 | 18 | 365 | No | |
| 90 | 19 | 403 | ||
| 91 | 20 | 443 | ||
| 92 | 21 | 485 | No |
The above table yields many prime numbers, which again can be put at the place of k and so on the table can be progressed.
According to Euler, 41 was the most appropriate value of k yielding more prime numbers than any other k. In the list below, each value of f(x) is a prime for k=41:
| k
41 |
x
0 |
f(x)
41 |
| 1 | 43 | |
| 2 | 47 | |
| 3 | 53 | |
| 4 | 61 | |
| 5 | 71 | |
| 6 | 83 | |
| 7 | 97 | |
| 8 | 113 | |
| 9 | 131 | |
| 10 | 151 | |
| 11 | 173 | |
| 12 | 197 | |
| 13 | 223 | |
| 14 | 251 | |
| 15 | 281 | |
| 16 | 313 | |
| 17 | 347 | |
| 18 | 383 | |
| 19 | 421 | |
| 20 | 461 | |
| 21 | 503 | |
| 22 | 547 | |
| 23 | 593 | |
| 24 | 641 | |
| 25 | 691 | |
| 26 | 743 | |
| 27 | 797 | |
| 28 | 853 | |
| 29 | 911 | |
| 30 | 971 | |
| 31 | 1033 | |
| 32 | 1097 | |
| 33 | 1163 | |
| 34 | 1231 | |
| 35 | 1301 | |
| 36 | 1373 | |
| 37 | 1447 | |
| 38 | 1523 | |
| 39 | 1601 |
So, the Euler’s Prime Generating Equation can be written as
Wait. What if we increase the value of x beyond the limit of 39? What will we get?
The next values of f(x) in this series would be 1681, 1763, 1847, 1933, 2021, 2111, 2203, 2297, 2393, … .
Are all these prime numbers too? The answer is no. 1681 is not a prime number, neither are 1763 and 2021. Though all others are prime numbers.
Why only mathematics?
This is the question, I asked myself.
Why only mathematics? Why so serious stuffs?
Why not have something new? New like adding more creativity and engaging more topics.
MY DIGITAL NOTEBOOK was aimed to be a notebook type blog, in which thoughts and useful class-notes were to be written. What happened? I quit writing here.
Statistical Mechanics: Ensembles
Statistical Mechanics
I have planned to bring my class notes on internet now. In this very first article, I’d like to put some light on Ensembles which are the most essential parts of Statistical Mechanics. After the introduction of Ensembles, we shall proceed to other important topics like μ and γ spaces, postulates of Statistical Mechanics, Liouville’s theorem, partition function etc. and much more. As always, I have tried my best to keep the language simple and graspable.
Analysis of Meteorological Data of Pantnagar Weather Station
About: This post is actually a summary of a research project I took under INSPIRE-SHE Scholarship Program by Dept. of Science and Technology, Govt. of India. My plan was to make the content open-source on the web that faults could be corrected by time. The language is simple and very easy to understand and the ease of understanding is focused to A-level (10+2) students and beyond.
