Thirteen (Transformers)

The Thirteen Original Transformers (sometimes referred to as the Thirteen Primes, the Dynasty of Primes or simply the Thirteen) are thirteen fictional characters in the Transformers toy and entertainment franchise created by Hasbro. They are usually portrayed as the first thirteen living beings created by Primus, the creator of the Transformers and their home planet of Cybertron. In the live-action Transformers film trilogy, their back-story is slightly modified, with there only being seven members who were created by the Allspark. The story concept of the Thirteen, as well as three of their members (Prima, Liege Maximo and The Fallen), were created by comic book writer Simon Furman.

Concept history

It was originally revealed in the Botcon story "Covenant" that before going on to create the Transformer race, Primus experimented with a group of twelve robots known as the Covenant of Primus. Based on the zodiac, these twelve robots were: Leonicus (leader), Aries, Piscor, Libras, Scorpius, Aquator, Taurotron, Cancix, Geminator, Sagittarii, Virgol and Capricurn . They existed in secret, training for the Omega Point. The Omega Point was a potential event that Unicron would attack at a point that there was no Prime. After the Omega Point, time was reverted and the instance never happened.

Prime number

A 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 . 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.

Primality test

A primality test is an algorithm for determining whether an input number is prime. Amongst other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests prove that a number is prime, while others like Miller–Rabin prove that a number is composite. Therefore, the latter might be called compositeness tests instead of primality tests.

Simple methods

The simplest primality test is trial division: Given an input number n, check whether any prime integer m from 2 to √n evenly divides n (the division leaves no remainder). If n is divisible by any m then n is composite, otherwise it is prime.

For example, we can do a trial division to test the primality of 100. Let's look at all the divisors of 100:

Transformers

Transformers (Japanese: トランスフォーマー, Hepburn: Toransufōmā) is a media franchise produced by American toy company Hasbro and Japanese toy company Takara Tomy. Initially a line of transforming toys rebranded from Takara's Diaclone and Microman toylines, the franchise began in 1984 with the Transformers toy line, and centers on factions of transforming alien robots (often the Autobots and the Decepticons) in an endless struggle for dominance or eventual peace. In its decades-long history, the franchise has expanded to encompass comic books, animation, video games and films.

The term "Generation 1" covers both the animated television series The Transformers and the comic book series of the same name, which are further divided into Japanese and British spin-offs, respectively. Sequels followed, such as the Generation 2 comic book and Beast Wars TV series, which became its own mini-universe. Generation 1 characters underwent two reboots with Dreamwave in 2001 and IDW Publishing in 2005, also as a remastered series. There have been other incarnations of the story based on different toy lines during and after the 20th-Century. The first was the Robots in Disguise series, followed by three shows (Armada, Energon, and Cybertron) that constitute a single universe called the "Unicron Trilogy". A live-action film was also released in 2007, with a sequel in 2009, a second sequel in 2011, and a third in 2014. again distinct from previous incarnations, while the Transformers: Animated series merged concepts from the G1 story-arc, the 2007 live-action film and the "Unicron Trilogy". Transformers: Prime previously aired on The Hub.

Transformers (2003 video game)

Transformers (トランスフォーマー, Toransufōmā), or The Transformers: Call of the Future, is an action role-playing game released by Takara in October 2003 for PlayStation 2 exclusively in Japan. It is based on the popular Transformers animated series. During early stages of development it was led to believe by the media that the game was called Transformers: Tataki (トランスフォーマー: タタキ, Toransufōmā: Tataki), or Transformers: Assault, a title that many fans use to help disambiguate.

Overview

The game allows players to select a side (either Autobot or Decepticon). The Autobot side stars Optimus Prime, Jazz and Wheeljack, who are later joined by Rodimus Prime, Arcee and Kup. The Decepticon faction begins with Megatron (referred to here by his Japanese title Emperor of Destruction), Starscream and Soundwave with Galvatron, Cyclonus and Scourge joining them later on. Other Transformers are unlocked as the game progresses and join their respective factions. These Transformers include such Generation 1 stalwarts as Ratchet, Bumblebee, Hound, Astrotrain, Blitzwing and Shockwave. Later additions from the Transformers movie, such as Springer and Ultra Magnus, also appear. A number of characters from the Japanese exclusive series The Headmasters make appearances as well, notably the Trainbots and Sixshot (who is portrayed as a powerful ninja warrior as he was in the Headmasters anime), also included were Dark Hot Rod (Black Rodimus) and Optimus Clone (Black Convoy).

List of Transformers TV series

Launched in 1984, Hasbro's Transformers toyline was promoted through both a comic book by Marvel Comics and an animated series produced by Sunbow Productions and Marvel Productions. Although the comic outlived the animated series by a number of years, it was the animated series that truly captured the hearts and minds of children worldwide. With the original show's conclusion in 1987, original series exclusive to Japan were created which ran until 1990, and the franchise was later re-imagined with the fully CGI Beast Wars in the late 1990s. The 21st Century saw a total reboot of the Transformers universe, as Hasbro collaborated with Japanese Transformers producers Takara to create a new storyline with Transformers: Armada and its sequels, produced in Japan and then dubbed for English-speaking audience. In 2008, Transformers Animated saw Hasbro take control of the franchise once more through collaboration with Cartoon Network, bringing writing duties back to America, with animation being handled by Japanese studios. Hasbro also reacquired the distribution rights to the original series from Sunbow finally giving them the complete rights to the series based on their Generation 1 toy-line.