Both Primes returned to the Ark ( the second secretly being controlled by Megatron ), causing confusion among the Autobot ranks.

where b is the number base ( 10 for decimal ), and p is a prime that does not divide b. ( Primes p that give cyclic numbers are called full reptend primes or long primes ).

* Priming ( media ) is a cognitive process, in which media information ( Primes ) increases temporarily the accessibility of knowledge units in the memory of an individual, which makes it more likely that these knowledge units are used in the reception, interpretation and judgement for the following external information.

" die Anzahl der Primzahlen unter einer gegebenen " ( usual English translation: " On the Number of Primes Less Than a Given Magnitude ") is a seminal 10-page paper by Bernhard Riemann published in the November 1859 edition of the Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin.

In the first season finale, it is mentioned that Optimus carries the Matrix within himself, and it carries the wisdom of the Thirteen Primes who preceded him.

Optimus wielding the Star Saber confronts Megatron, and discovers Megatron had the right hand of a deceased Prime attached to himself in order to use the Forge of Solus Prime to create his own sword the " Dark Star Saber " ( which Megatron calls the Slayer of Primes ) which is forged of Dark Energon ( the blood of Unicorn ).

Alpha Trion is one of the Thirteen Primes, thus all his portrayals are considered to be the same individual.

Hasbro has registered the name Alpha Trion for Trademark in the U. S. Alpha Trion's status as one of the Thirteen is a retroactive alteration to the character's history, as the Thirteen Primes are a later concept developed in the Transformers franchise, and as such the concept was not referenced in the Generation One continuities.

He is one of the Thirteen Primes who defeated Unicron.

Alpha Trion is an archivist and one of the Thirteen Primes.

An appeal that a mathematical definition is in itself wrong ( i. e., that primes were somehow poorly defined in the first place ) is an appeal to an argument that attacks a well-established and well-understood definition: Primes are prime by definition, and such classes of numbers may or may not have properties that make them interesting.

A significant new mechanic is the notion of " Primes ", often referred to by gamers as the 12 / 18 system.

In his 1859 paper On the Number of Primes Less Than a Given Magnitude Riemann found an explicit formula for the normalized prime-counting function π < sub > 0 </ sub >( x ) which is related to the prime-counting function π ( x ) by

That is, p and q must be of the form 4t + 3, for some integer t. Primes of this form are referred to as Blum primes.

In this continuity, Vector Prime is also one of the Thirteen Primes.

Megatronus is mentioned as one of the original thirteen Primes.

However, it is revealed that the Primes are planning a much larger invasion, which humanity will be all but powerless to stop.

Metroid Primes style of gameplay and HUDs also led to influence and comparison in later first-person shooters, such as Geist and Star Wars: Republic Commando.

* Top-20 Twin Primes at Chris Caldwell's Prime Pages.

However, in doing so, not only did he lose the collective wisdom of the Primes, but lost his own memories as a Prime, thus causing Optimus to believe he was still Orion Pax, his previous identity.

Alpha Trion tells Optimus Prime about the Covenant of Primes tells him about the future, but not what the outcome will be.

* Chris Caldwell, The Largest Known Primes at The Prime Pages.

Human resistance forces have found two ways to fight back: using the Prime weapons ( primarily directed-energy weapons ) against the invaders, and disrupting communication between the slave caste ( motiles ) and the commanding caste ( immotiles ) of the Primes.

* Chapter 3: Recognizing Primes and Composites, pp. 109 – 158.

: 1. Chen primes were first described by Yuan, W. On the Representation of Large Even Integers as a Sum of a Product of at Most 3 Primes and a Product of at Most 4 Primes, Scienca Sinica 16, 157-176, 1973.

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.

Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper On the Number of Primes Less Than a Given Magnitude, in which he defined his zeta function and proved its basic properties.

However, before departing to Earth's core, Optimus entrusted the Key to Vector Sigma to Jack Darby, a means to restore his memories as well as the Matrix, as Vector Sigma contained not only the memories of Optimus, but those of any and all holders of the Matrix, which in this continuity appears to be only the original thirteen Primes and Optimus himself.

In Factors the muncher seeks to ingest the factors of a given number, in Primes he craves prime numbers, and in the Equality and Inequality modes the muncher devours expressions such as 2 + 4 which are equivalent or not equivalent ( respectively ) to the designated number.

The Dynasty of Primes had one rule: Solar Harvesters were not to be built in systems which contain life.

Section 4. 5. 4: Factoring into Primes, pp. 379 – 417.

Without doubt, the single most significant paper concerning the distribution of prime numbers was Riemann's 1859 memoir On the Number of Primes Less Than a Given Magnitude, the only paper he ever wrote on the subject.

Bernhard Riemann in his memoir " On the Number of Primes Less Than a Given Magnitude " published in 1859 extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation and established a relation between its zeros and the distribution of prime numbers.

The functional equation was established by Riemann in his 1859 paper On the Number of Primes Less Than a Given Magnitude and used to construct the analytic continuation in the first place.

Semantic Primes and Universal Grammar: Empirical evidence from the Romance languages.

Semantics: Primes and Universals.

They will later join with The Primes and become The Temptations.

The very strongest are employed as " T1 Primes " by an independent company, FT & T, ( Federated Telepaths and Teleporters ) for teleporting cargo and passengers between the systems.

She wasn't empathic towards the child and instilled a neurosis ( a form of agoraphobia that prevents interstellar teleports ) in the three Primes that she trained.

Primes of FT & T are T-1 telekinetic / telepaths.

Three New Mersenne Primes and a Statistical Theory, Mathematics of Comput., Vol.

Milton Jenkins, a local man then best known for his work with the all-male group the Primes ( who became The Temptations ), was scouting for girls to become members of his group's sister act, the Primettes.

Eighteen-year-old Betty McGlown, who was dating Primes member Paul Williams at the time, rounded out the quartet.

With this sacrifice, he not only loses the Wisdom of the Primes but also his memories of the war and his comrades, and joins Megatron as a Decepticon under his old name, Orion Pax.

* Wierzbicka, Anna, Semantics: Primes and Universals ( 1996 ), Oxford: Oxford University Press, 2004.

When Milton Jenkins, manager of male vocal group The Primes, decided to form a female spin-off group called The Primettes, he recruited Ballard, who recruited Wilson.