Goldbach's conjecture.

           

Goldbach's conjecture.

Numbers between 30 and 50 as a product of primes.

Prime Numbers - biggest prime number so far.

Prime Numbers - biggest prime number so far.

Largest known prime number. As of January 2016 , the largest known prime number is2^74,207,281 − 1, a number with 22,338,618decimal digits. It was found in 2016 by the Great Internet Mersenne Prime Search (GIMPS). Plot of the number of digits in largest known prime by year, since the electronic computer.

list of primes from internet

Prime numbers - Sieve of Eratosthanes

Prime numbers.

 List of all the prime numbers between 1 and 100 using the Sieve of Eratosthanes.

4.2)Randoms

 This is the longest list of randoms  between 1 and 100 you can do in Excel using RANDBETWEEN().

4.1)Randoms

Randoms

Using Excel, create random numbers between 1 and 100 and a chart. 

Logic gates

Task - Web page.

     My webpage about the history of numbers 

Prime numbers

History of prime Numbers

prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3.The property of being prime (or not) is called primality. A simple but slow method of verifying the primality of a given number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and \sqrt{n}. Algorithms much more efficient than trial division have been devised to test the primality of large numbers. These include the Miller–Rabin primality test, which is fast but has a small probability of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits.
There are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no known simple formula that separates prime numbers from composite numbers. However, the distribution of primes, that is to say, the statistical behaviour of primes in the large, can be modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability that a given, randomly chosen number n is prime is inversely proportional to its number of digits, or to the logarithm of n.
Many questions regarding prime numbers remain open, such as Goldbach's conjecture (that every even integer greater than 2 can be expressed as the sum of two primes), and the twin prime conjecture (that there are infinitely many pairs of primes whose difference is 2). Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which makes use of properties such as the difficulty of factoring large numbers into their prime factors. Prime numbers give rise to various generalizations in other mathematical domains, mainly algebra, such as prime elements and prime ideals.

Definition and examples

A natural number (i.e. 1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it has exactly two positive divisors, 1 and the number itself.[1] Natural numbers greater than 1 that are not prime are called composite. Among the numbers 1 to 6, the numbers 2, 3, and 5 are the prime numbers, while 1, 4, and 6 are not prime. 1 is excluded as a prime number, for reasons explained below. 2 is a prime number, since the only natural numbers dividing it are 1 and 2. Next, 3 is prime, too: 1 and 3 do divide 3 without remainder, but 3 divided by 2 gives remainder 1. Thus, 3 is prime. However, 4 is composite, since 2 is another number (in addition to 1 and 4) dividing 4 without remainder:
4 = 2 · 2. 5 is again prime: none of the numbers 2, 3, or 4 divide 5. Next, 6 is divisible by 2 or 3, since
6 = 2 · 3. Hence, 6 is not prime. The image at the right illustrates that 12 is not prime: 12 = 3 · 4. No even number greater than 2 is prime because by definition, any such number n has at least three distinct divisors, namely 1, 2, and n. This implies that n is not prime. Accordingly, the term odd prime refers to any prime number greater than 2. Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9, since even numbers are multiples of 2 and numbers ending in 0 or 5 are multiples of 5.
If n is a natural number, then 1 and n divide n without remainder. Therefore, the condition of being a prime can also be restated as: a number is prime if it is greater than one and if none of 2, 3, ..., n - 1 divides n (without remainder). Yet another way to say the same is: a number n > 1 is prime if it cannot be written as a product of two integers a and b, both of which are larger than 1: n = a · b. In other words, n is prime if n items cannot be divided up into smaller equal-size groups of more than one item. The set of all primes is often denoted by P.
The first 168 prime numbers (all the prime numbers less than 1000) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 (sequence A000040 in OEIS).

Fundamental theorem of arithmetic

The crucial importance of prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic, which states that every integer larger than 1 can be written as a product of one or more primes in a way that is unique except for the order of the prime factors.[2] Primes can thus be considered the “basic building blocks” of the natural numbers..

Primality of one

Most early Greeks did not even consider 1 to be a number,[4] so they could not consider it to be a prime. By the Middle Ages and Renaissance many mathematicians included 1 as the first prime number.[5] In the mid-18th century Christian Goldbach listed 1 as the first prime in his famous correspondence with Leonhard Euler -- who did not agree.[6] In the 19th century many mathematicians still considered the number 1 to be a prime. For example, Derrick Norman Lehmer's list of primes up to 10,006,721, reprinted as late as 1956,[7] started with 1 as its first prime.[8] Henri Lebesgue is said to be the last professional mathematician to call 1 prime.[9] By the early 20th century, mathematicians began to accept that 1 is not a prime number, but rather forms its own special category as a "unit".[5] A large body of mathematical work would still be valid when calling 1 a prime, but Euclid's fundamental theorem of arithmetic (mentioned above) would not hold as stated. For example, the number 15 can be factored as 3 · 5 and 1 · 3 · 5; if 1 were admitted as a prime, these two presentations would be considered different factorizations of 15 into prime numbers, so the statement of that theorem would have to be modified. Similarly, the sieve of Eratosthenes would not work correctly if 1 were considered a prime: a modified version of the sieve that considers 1 as prime would eliminate all multiples of 1 (that is, all other numbers) and produce as output only the single number 1. Furthermore, the prime numbers have several properties that the number 1 lacks, such as the relationship of the number to its corresponding value of Euler's totient function or the sum of divisors function.[10]

Prime numbers

 Here is the list of Primary Numbers from one to 100

Sieve of Eratosthanes

     Sieve of Eratosthenes

How the Sieve of Eratosthenes works?

When the multiples sublime, the numbers that reman are prime. A prime number is a natural number that has exactly two district natural number divisions. 1 and itself.

Here is a good video explaining how does de Sieve of Eratosthenes work.

Task 26

Task 26 modified

Task 25.2

Quotation Tag/ changed 

Task 25

Small changes on the last task on the list 

200 words about myself

Here is a task called "200 words about myself", all done and handle it :) Another one out of my list!

MS World Assignment

Task Done.

MS World called "My favorite Sites" done and handle it. 

Define Tag.

Define Tag

Tag

"A command inserted in a document that specifies how the document, or a portion of the document, should be formatted. Tags are used by all format specifications that store documents as text files. This includes SGML and HTML.

(v) To mark a section of a document with a formatting command". (Webopedia)

There are many tag options for any single command. One of my favorite tag is the <img> (image tag). This tag can do so much for a webpage, can you imagine an website without any pictures or even a nice background? Would be boring and tiring that's for sure. 

Best Browser 

Sometimes find a browser that respond is a little bit hard. Speed issues is one of the main resons why people get frustrated on front of computer. For me, its all about privacy and speed. Here is the two browsers i recommend.

Mozilla Firefox (or simply Firefox) is a free and open-source^[21]web browser developed by the Mozilla Foundation and its subsidiary, the Mozilla Corporation. Firefox is available forWindows, OS X and Linux operating systems, with its mobile versions available for Android, and Firefox OS; where all of these versions use the Gecko layout engine to render web pages, which implements current and anticipated web standards,^[22] but an additional version released in late 2015 – Firefox for iOS has also been made available – that doesn't use Gecko.

Firefox was created in 2002, under the name "Phoenix" by theMozilla community members who wanted a standalone browser rather than the Mozilla Application Suite bundle. Even during itsbeta phase, Firefox proved to be popular by its testers and was praised for its speed, security and add-ons compared to Microsoft's then-dominant Internet Explorer 6. Firefox was released in November 2004,^[23] and was highly successful with 60 million downloads within nine months, which was the first time that Internet Explorer's dominance was challenged.^[24] Firefox is considered thespiritual successor of Netscape Navigator,^[25] as the Mozilla community was created by Netscape in 1998 before their acquisition by AOL.^[26]

Google Chrome is a freeware web browser^[11] developed byGoogle. It used the WebKit layout engine until version 27 and with the exception of its iOS releases, from version 28 and beyond uses the WebKit fork Blink.^[12][13][14] It was first released as a beta version for Microsoft Windows on September 2, 2008, and as a stable public release on December 11, 2008.

As of December 2015, StatCounter estimates that Google Chrome has a 58% worldwide usage share of web browsers as a desktop browser.^[15] It is also the most popular browser for smartphones, and combined across all platforms at about 45%. Its success has led to Google expanding the 'Chrome' brand name on various other products such as the Chromecast.

So, this is my two favorites. Credits to Wikipedia.

The <img> Tag

Here is a simple description of when and how to use the image tag. Information from W3 schools

The <img> tag defines an image in an HTML page.

The <img> tag has two required attributes: src and alt.

Note: Images are not technically inserted into an HTML page, images are linked to HTML pages. The <img> tag creates a holding space for the referenced image.

Tip: To link an image to another document, simply nest the <img> tag inside <a> tags.

For me, the <img> tag is one of the most importances. How to make a webpage prettier? Webpages are built to help people, business, etc... In this case, images are an very important toll to create an interesting page. 

Task 24

 Making small changes on HTML

Here is the example without changes 

Here i used the <i> tag and the <b>

Task 22

Small changes

Small changes

Small changes

Task 20

Task 20 asked to write a little bit about me, so here we are

Task 17a

Changes in HTML file

Editor from W3schools

And changes i made n this document.

I personally found those tags easy to memorize, change background color and font color is reasonable easy to use, it gives the page a new look and you can play with colors and fonts.

Task 15 (underline, italics and bold)

Here is the screenshot of my trial using the <b>, <i> and the .<p> tag

Those tags are really easy to use and i also added a picture (Img) form the internet

Task 14 HTML Editors

HTML Editors 

Some great online HTML editors, i personally liked this one for one simple reason. EASY to use and well design.

HTML-online.com

Another excellent option is the online HTML editor.Net, very useful and clean. 

Online HTML.net

Task 12 HTML Paragraphs script

Paragraph Script for HTML.

The paragraphs tags are used to define a block of a txt as a paragraphs 

Paragraph Script  

Task 11 HTML Headings Script

HTML Headings script sample. I used different information for different heading  

Task 8

Running it through a browser 

<html>
<head>
<title>My First Page,</Title>
</head>
</html>

HTML Task 10

Task 10

HTML Class. Learning HTML using ww.w3schools.com.

This is one of my first trials using the HTML editor, the program is great with loads of ideas and different ways of how to learn and manager HTML easily.

Task 4 w3schools HTML

What a great website :)
Want to learn more about HTML? Just like that, simple and easy.


http://www.w3schools.com/html/html_examples.asp

A little bit about me

My name is Evelyn Araujo and i'm originally from Brazil ( South America). I arrive in NZ all most 10 years ago to explore the natural resources this place has to offer and i became in love!
I was studying Electrical engineering back in my country and Technology had always been part of my life.

I'm also a formed Violin/ Viola player, i grew up in a family of engineers and musicians and being around IT and Music is something i'm used to it.  This Blog will give me the opportunity to show what i'm up to and to share my work with others.