# Synonyms containing **prime connections**

### We've found **33,453** synonyms:

Bicommutant | Bicommutant In algebra, the bicommutant of a subset S of a semigroup (such as an algebra or a group) is the commutant of the commutant of that subset. It is also known as the double commutant or second commutant and is written S ′ ′ {\displaystyle S^{\prime \prime }} . The bicommutant is particularly useful in operator theory, due to the von Neumann double commutant theorem, which relates the algebraic and analytic structures of operator algebras. Specifically, it shows that if M is a unital, self-adjoint operator algebra in the C*-algebra B(H), for some Hilbert space H, then the weak closure, strong closure and bicommutant of M are equal. This tells us that a unital C*-subalgebra M of B(H) is a von Neumann algebra if, and only if, M = M ′ ′ {\displaystyle M=M^{\prime \prime }} , and that if not, the von Neumann algebra it generates is M ′ ′ {\displaystyle M^{\prime \prime }} . The bicommutant of S always contains S. So S ′ ′ ′ = ( S ′ ′ ) ′ ⊆ S ′ {\displaystyle S^{\prime \prime \prime }=\left(S^{\prime \prime }\right)^{\prime }\subseteq S^{\prime }} . On the other hand, S ′ ⊆ ( S ′ ) ′ ′ = S ′ ′ ′ {\displaystyle S^{\prime }\subseteq \left(S^{\prime }\right)^{\prime \prime }=S^{\prime \prime \prime }} . So S ′ = S ′ ′ ′ {\displaystyle S^{\prime }=S^{\prime \prime \prime }} , i.e. the commutant of the bicommutant of S is equal to the commutant of S. — Wikipedia |

Prime factor | Prime factor In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. The process of finding these numbers is called integer factorization, or prime factorization. A prime factor can be visualized by understanding Euclid's geometric position. He saw a whole number as a line segment, which has a smallest line segment greater than 1 that can divide equally into it. For a prime factor p of n, the multiplicity of p is the largest exponent a for which pa divides n. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicity. The fundamental theorem of arithmetic says that every positive integer has a unique prime factorization. To shorten prime factorization, numbers are often expressed in powers, so For a positive integer n, the number of prime factors of n and the sum of the prime factors of n are examples of arithmetic functions of n that are additive but not completely additive. Determining the prime factors of a number is an example of a problem frequently used to ensure cryptographic security in encryption systems; this problem is believed to require super-polynomial time in the number of digits — it is relatively easy to construct a problem that would take longer than the known age of the Universe to solve on current computers using current algorithms. — Freebase |

Palindromic prime | Palindromic prime A palindromic prime is a prime number that is also a palindromic number. Palindromicity depends on the base of the numbering system and its writing conventions, while primality is independent of such concerns. The first few decimal palindromic primes are: Except for 11, all palindromic primes have an odd number of digits, because the divisibility test for 11 tells us that every palindromic number with an even number of digits is a multiple of 11. It is not known if there are infinitely many palindromic primes in base 10. The largest known as of January 2013 is 10314727 - 8×10^157363 - 1, found by Harvey Dubner. On the other hand, it is known that, for any base, almost all palindromic numbers are composite. In binary, the palindromic primes include the Mersenne primes and the Fermat primes. All binary palindromic primes except binary 11 have an odd number of digits; those palindromes with an even number of digits are divisible by 3. The sequence of binary palindromic primes begins: Ribenboim defines a triply palindromic prime as a prime p for which: p is a palindromic prime with q digits, where q is a palindromic prime with r digits, where r is also a palindromic prime. For example, p = 1011310 + 4661664×10^5,652 + 1, which has q = 11311 digits, and 11311 has r = 5 digits. The first triply palindromic prime is the 11-digit 10000500001. It's possible that a triply palindromic prime in base 10 may also be palindromic in another base, such as base 2, but it would be highly remarkable if it were also a triply palindromic prime in that base as well. — Freebase |

Schottky defect | Schottky defect A Schottky defect is a type of point defect in a crystal lattice named after Walter H. Schottky. In non-ionic crystals it means a lattice valency defect. In ionic crystals, this point defect forms when oppositely charged ions leave their lattice sites, creating vacancies. These vacancies are formed in stoichiometric units, to maintain an overall neutral charge in the ionic solid. The surrounding atoms then move to fill these vacancies, causing new vacancies to form. Normally these defects will lead to a decrease in the density of the crystal or metal. Chemical equations in Kröger–Vink notation for the formation of Schottky defects in TiO2 and BaTiO3. ∅ ⇌ v ′ ′ ′ ′ {\displaystyle \prime \prime \prime \prime } Ti + 2 v••O∅ ⇌ v ′ ′ {\displaystyle \prime \prime } Ba + v ′ ′ ′ ′ {\displaystyle \prime \prime \prime \prime } Ti + 3 v••OThis can be illustrated schematically with a two-dimensional diagram of a sodium chloride crystal lattice: — Wikipedia |

TWINKLE | TWINKLE TWINKLE is a hypothetical integer factorization device described in 1999 by Adi Shamir and purported to be capable of factoring 512-bit integers. The name is an acronym of "The Weizmann Institute Key Locating Engine". It is also a pun on the twinkling LEDs used in the device. The goal of TWINKLE is to implement the sieving step of the Number Field Sieve algorithm, which is the fastest known algorithm for factoring large integers. The sieving step, at least for 512-bit and larger integers, is the most time consuming step of NFS. It involves testing a large set of numbers for B-'smoothness', i.e., absence of a prime factor greater than a specified bound B. What is remarkable about TWINKLE is that it is not a purely digital device. It gets its efficiency by eschewing binary arithmetic for an "optical" adder which can add hundreds of thousands of quantities in a single clock cycle. The key idea used is "time-space inversion". Conventional NFS sieving is carried out one prime at a time. For each prime, all the numbers to be tested for smoothness in the range under consideration which are divisible by that prime have their counter incremented by the logarithm of the prime. TWINKLE, on the other hand, works one candidate smooth number at a time. There is one LED corresponding to each prime smaller than B. At the time instant corresponding to X, the set of LEDs glowing corresponds to the set of primes that divide X. This can be accomplished by having the LED associated with the prime p glow once every p time instants. Further, the intensity of each LED is proportional to the logarithm of the corresponding prime. Thus, the total intensity equals the sum of the logarithms of all the prime factors of X smaller than B. This intensity is equal to the logarithm of X if and only if X is B-smooth. — Freebase |

synchromysticism | synchromysticism The drawing of connections in modern culture (movies, music lyrics, historical happenings and esoteric knowledge); and finding connections that could be coming from the "collective unconscious mind"; and finding connections between occult knowledge (i.e. esoteric fraternities, cults and secret rituals), politics and mass media. — Wiktionary |

Twin prime | Twin prime A twin prime is a prime number that differs from another prime number by two, for example the twin prime pair. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Twin primes appear despite the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger due to the prime number theorem. — Freebase |

Ehud Olmert | Ehud Olmert Ehud Olmert is an Israeli politician and lawyer. He served as Prime Minister of Israel from 2006 to 2009 and before that as a cabinet minister from 1988 to 1992 and from 2003 to 2006. Between his first and second stints as a cabinet member, he served as mayor of Jerusalem from 1993 to 2003. In 2003 Olmert was re-elected to the Knesset, and became a cabinet minister and acting prime minister in the government of Prime Minister Ariel Sharon. On 4 January 2006, after Sharon suffered a severe hemorrhagic stroke, Olmert began exercising the powers of the office of Prime Minister. Olmert led Kadima to a victory in the March 2006 elections, and continued on as Acting Prime Minister. On 14 April, two weeks after the election, Sharon was declared permanently incapacitated, allowing Olmert to legally become Interim Prime Minister. Less than a month later, on 4 May, Olmert and his new, post-election government were approved by the Knesset, thus Olmert officially became prime minister of Israel. Olmert and his government enjoyed healthy relations with the Fatah-led Palestinian National Authority, which culminated in November 2007 at the Annapolis Conference. However, during his tenure as prime minister, there were major military conflicts with both Hezbollah and Hamas. Olmert and Minister of Defense Amir Peretz were heavily criticized for their handling of the 2006 Lebanon War. In late 2008, a ceasefire between Hamas and Israel ended, which led to the 2008–2009 Israel–Gaza conflict. Olmert declared that the Israeli Defense Force would target the Hamas leadership and infrastructure in the war. — Freebase |

Super-prime | Super-prime Super-prime numbers are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins That is, if p denotes the ith prime number, the numbers in this sequence are those of the form p. Dressler & Parker used a computer-aided proof to show that every integer greater than 96 may be represented as a sum of distinct super-prime numbers. Their proof relies on a result resembling Bertrand's postulate, stating that each super-prime number is less than twice its predecessor in the sequence. Broughan and Barnett show that there are super-primes up to x. This can be used to show that the set of all super-primes is small. One can also define "higher-order" primeness much the same way, and obtain analogous sequences of primes. Fernandez A variation on this theme is the sequence of prime numbers with palindromic indices, beginning with — Freebase |

Rainilaiarivony | Rainilaiarivony Rainilaiarivony (30 January 1828 – 17 July 1896) was a Malagasy politician who served as the Prime Minister of Madagascar from 1864 to 1895, succeeding his older brother Rainivoninahitriniony, who had held the post for thirteen years. His career mirrored that of his father Rainiharo, a renowned military man who became Prime Minister during the reign of Queen Ranavalona I. Despite a childhood marked by ostracism from his family, as a young man Rainilaiarivony was elevated to a position of high authority and confidence in the royal court, serving alongside his father and brother. He co-led a critical military expedition with Rainivoninahitriniony at the age of 24 and was promoted to Commander-in-Chief of the army following the death of the queen in 1861. In that position he oversaw continuing efforts to maintain royal authority in the outlying regions of Madagascar and acted as adviser to his brother, who had been promoted to Prime Minister in 1852. He also influenced the transformation of the kingdom's government from an absolute monarchy to a constitutional one, in which power was shared between the sovereign and the Prime Minister. Rainilaiarivony and Queen Rasoherina worked together to depose Rainivoninahitriniony for his abuses of office in 1864. Taking his brother's place as Prime Minister, Rainilaiarivony remained in power as Madagascar's longest-serving prime minister for the next 31 years by marrying three queens in succession: Rasoherina, Ranavalona II and Ranavalona III. As Prime Minister, Rainilaiarivony actively sought to modernize the administration of the state, in order to strengthen and protect Madagascar against the political designs of the British and French colonial empires. The army was reorganized and professionalized, public schooling was made mandatory, a series of legal codes patterned on English law were enacted and three courts were established in Antananarivo. The statesman exercised care not to offend traditional norms, while gradually limiting traditional practices, such as slavery, polygamy, and unilateral repudiation of wives. He legislated the Christianization of the monarchy under Ranavalona II. His diplomatic skills and military acumen assured the defense of Madagascar during the Franco-Hova Wars, successfully preserving his country's sovereignty until a French column captured the royal palace in September 1895. Although holding him in high esteem, the French colonial authority deposed the Prime Minister and exiled him to French Algeria, where he died less than a year later in August 1896. — Wikipedia |

Prime number theorem | Prime number theorem In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is π(N) ~ N/log(N), where π(N) is the prime-counting function and log(N) is the natural logarithm of N. This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N). Consequently, a random integer with at most 2n digits (for large enough n) is about half as likely to be prime as a random integer with at most n digits. For example, among the positive integers of at most 1000 digits, about one in 2300 is prime (log(101000) ≈ 2302.6), whereas among positive integers of at most 2000 digits, about one in 4600 is prime (log(102000) ≈ 4605.2). In other words, the average gap between consecutive prime numbers among the first N integers is roughly log(N). — Wikipedia |

Holonomy | Holonomy In differential geometry, the holonomy of a connection on a smooth manifold is a general geometrical consequence of the curvature of the connection measuring the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported. For flat connections, the associated holonomy is a type of monodromy, and is an inherently global notion. For curved connections, holonomy has nontrivial local and global features. Any kind of connection on a manifold gives rise, through its parallel transport maps, to some notion of holonomy. The most common forms of holonomy are for connections possessing some kind of symmetry. Important examples include: holonomy of the Levi-Civita connection in Riemannian geometry, holonomy of connections in vector bundles, holonomy of Cartan connections, and holonomy of connections in principal bundles. In each of these cases, the holonomy of the connection can be identified with a Lie group, the holonomy group. The holonomy of a connection is closely related to the curvature of the connection, via the Ambrose–Singer theorem. The study of Riemannian holonomy has led to a number of important developments. The holonomy was introduced by Cartan in order to study and classify symmetric spaces. It was not until much later that holonomy groups would be used to study Riemannian geometry in a more general setting. In 1952 Georges de Rham proved the de Rham decomposition theorem, a principle for splitting a Riemannian manifold into a Cartesian product of Riemannian manifolds by splitting the tangent bundle into irreducible spaces under the action of the local holonomy groups. Later, in 1953, M. Berger classified the possible irreducible holonomies. The decomposition and classification of Riemannian holonomy has applications to physics, and in particular to string theory. — Freebase |

Sieve of Eratosthenes | Sieve of Eratosthenes In mathematics, the sieve of Eratosthenes, one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite the multiples of each prime, starting with the multiples of 2. The multiples of a given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. The sieve of Eratosthenes is one of the most efficient ways to find all of the smaller primes. It is named after Eratosthenes of Cyrene, a Greek mathematician; although none of his works have survived, the sieve was described and attributed to Eratosthenes in the Introduction to Arithmetic by Nicomachus. — Freebase |

Ridley | Ridley Ridley is a video game villain for the Metroid series. He is a dragon-like extraterrestrial that acts as Samus Aran's nemesis due to his attack on her homeworld; despite being killed multiple times by her, he is always revived by the Space Pirates continuously feeding him Bio-Matter. Originally appearing as a subordinate of Mother Brain, the primary antagonist of multiple titles in the Metroid series, he appears in Metroid Prime and Prime 3 by himself in his Meta Ridley form. Despite his monstrous appearance, he is revealed to be very intelligent and capable of speech in the Metroid e-manga, though he does not speak in the Metroid video games. Ridley originally appeared in the Nintendo Entertainment System video game Metroid. Mike Sneath, one of three senior character artists for Metroid Prime, was responsible for designing the Meta Ridley version of Ridley seen in Metroid Prime. It took him about "20 to 25 days" to model and texture Meta Ridley, citing the wings as having taken a few days of his time, commenting that it took him a while to get the shaders to work to give his wings the appearance of having a "holographic energy". He was not involved with designing the battle with Meta Ridley, which was left up to the game designers. Andrew Jones, the lead concept artist for Metroid Prime, had little to do with the design of Ridley. The initial design submitted was rejected by Nintendo, while the second design the artists submitted was approved. Steve Barcia, the executive producer of Retro Studios, called Ridley his favorite enemy from Metroid Prime due to the quality of the battle and his fan appeal. He added that such a battle was rare for a first person shooter, which helped to set Metroid Prime apart. Ridley also appears in Metroid: Other M. — Freebase |

Global Connections | Global Connections Global Connections is a charitable organisation acting as a UK network of mission agencies, churches, colleges and support agencies involved in evangelism around the world. Amongst the several hundred organisations and churches that are members of the Global Connections network are many of the most prominent Christian faith-based organisations as well as many major organisations involved in relief and development. The mission statement for the Global Connections network reads: "Mission at the heart of the church, the church at the heart of mission." Global Connections sees encouraging churches to become more involved in global issues, including world mission, as one of its key purposes. As part of this they seek to provide opportunities for church leaders to engage with the leaders of mission agencies. Global Connections also endeavours to bring together those who work in similar areas or to direct them to where they can find help on practical, legal or missiological issues. As part of this they organise approximately 20 forums, where members can meet with and learn from those who share similar concerns and can become involved in joint projects and co-operative actions. — Freebase |