The Jews for 2500 years have been a prime example, though the adherents of any world or interpeople religion are cases in point.

There seems to be an unfortunate assumption that an hour of Chicago-style jazz in prime evening time, for example, could not be justified without the trimmings of a portentous documentary.

A simple example is that almost all prime numbers are odd.

For example, the prime number theorem states that the number of prime numbers less than or equal to N is asymptotically equal to N / ln N. Therefore the proportion of prime integers is roughly 1 / ln N, which tends to 0.

An example is the " divides " relation between the set of prime numbers P and the set of integers Z, in which every prime p is associated with every integer z that is a multiple of p ( and not with any integer that is not a multiple of p ).

For example, the set with elements 2, 3, and 5 is equal to the set of all prime numbers less than 6.

In some applications it is useful to be able to compute the Bernoulli numbers B < sub > 0 </ sub > through B < sub > p − 3 </ sub > modulo p, where p is a prime ; for example to test whether Vandiver's conjecture holds for p, or even just to determine whether p is an irregular prime.

A prime example of bistability in biological systems is that of Sonic hedgehog ( Shh ), a secreted signaling molecule, which plays a critical role in development.

The 1951 children's film Duck and Cover is a prime example.

A prime example is in the case of Street Fighter X Tekken, where 12 characters advertised as downloadable content were found completed within the disc.

For example, the Riemann hypothesis is a conjecture from number theory that ( amongst other things ) makes predictions about the distribution of prime numbers.

" Despite having the quote presented to a notable organisation, it has also appeared in books such as " The Most Stupid Words Ever Spoken " as it is deemed by some Westerners as a prime example of a lack of understanding of foreign culinary traditions in the Western world.

The Chicago Building by Holabird & Roche ( 1904-1905 ) is a prime example of the Chicago School, displaying both variations of the Chicago window

In Unix-like operating systems, many files have no direct association with a physical storage device: < tt >/ dev / null </ tt > is a prime example, as are just about all files under < tt >/ dev </ tt >, < tt >/ proc </ tt > and < tt >/ sys </ tt >.

For example, primality testing is the problem of determining whether a given number is prime or not.

The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:

Virginia's " Technology Corridor " is a prime example of this activity.

Reduction modulo p ( which is needed for addition and multiplication ) can be executed much faster if the prime p is a pseudo-Mersenne prime that is, for example, or Compared to Barrett reduction there can be an order of magnitude speedup.

For example, neither 6 nor 35 is a prime number, since they both have two prime factors: 6 = 2 × 3 and 35 = 5 × 7.

Such payments shall be made to small domestic producers of zinc as long as the market price for prime western zinc at East Saint Louis, Illinois, as determined by the Secretary, is below 14-1/2 cents per pound, and such payments shall be 55 per centum of the difference between 14-1/2 cents per pound and the average market price for the month in which the sale occurred as determined by the Secretary.

In such cases it is the prime minister who holds the day-to-day powers of governance, while the King or Queen ( or other monarch, such as a Grand Duke, in the case of Luxembourg, or Prince in the case of Monaco and Liechtenstein ) retains only residual ( but not always minor ) powers.

In semi-presidential systems such as France, where the president formally appoints a prime minister but the government itself must still maintain the confidence of parliament, coalition governments occur quite regularly.

Of its factors, 2 and 3 are prime, which means the reciprocals of all 3-smooth numbers ( such as 2, 3, 4, 6, 8, 9 ...) have a terminating representation in duodecimal.

Notions such as prime numbers and rational and irrational numbers are introduced.

A key authoritarian element of fascism is its endorsement of a prime national leader, who is often known simply as the " Leader " or a similar title, such as Duce in Italian, Führer in German, Caudillo in Spanish, Poglavnik in Croatia, or Conducător in Romanian.

The best-known FFT algorithms depend upon the factorization of N, but there are FFTs with O ( N log N ) complexity for all N, even for prime N. Many FFT algorithms only depend on the fact that is an th primitive root of unity, and thus can be applied to analogous transforms over any finite field, such as number-theoretic transforms.

The president retains strong powers, such as authority to dissolve the National Assembly, declare a state of siege, delay legislation, conduct referendums, and appoint and dismiss the prime minister and cabinet members.

The Brontës ' fiction is seen by some feminist critics as prime examples of Female Gothic, exploring woman's entrapment within domestic space and subjection to patriarchal authority and the transgressive and dangerous attempts to subvert and escape such restriction.

that may give a head of state or their representative additional powers in unexpected circumstances ( such as the dismissal of Australian prime minister Gough Whitlam by Governor-General Sir John Kerr.

In Hinduism, certain dynasties adopted a title expressing their positions as " servant " of a patron deity of the state, but in the sense of a ( prime ) minister under a figure head of state, ruling " in the name of " the patron god ( ess ), such as Patmanabha Dasa ( servant of Vishnu ) in the case of the Maharaja of Travancore.

The settlers introduced chambered cairn tombs from around 3500 BC ( Maeshowe offers a prime example ), and from about 3000 BC the many standing stones and circles such as the Ring of Brodgar on Orkney and Callanish on Lewis.

This earned him the title of chief of engineering, amongst other essential titles such as prime minister, crown prince and head of the Royal Court.

# If a and p are natural numbers such that a < sup > p </ sup > − 1 is prime, then a

When Napoleon rose to power in 1799, there was no ancient base from which to draw his staff, and he had to choose the people he thought best for the job, including officers from his army, revolutionaries who had been in the National Assembly, and even some former aristocrats such as prime minister Talleyrand.

Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory.

Many questions around prime numbers remain open, such as Goldbach's conjecture, which asserts that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, which says that there are infinitely many pairs of primes whose difference is 2.

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.

Although he was a prime architect of the Vietnam War and repeatedly overruled the JCS on strategic matters, McNamara gradually became skeptical about whether the war could be won by deploying more troops to South Vietnam and intensifying the bombing of North Vietnam, a claim he would publish in a book years later.

* Mathematics: A group at the Indian Institute of Technology Kanpur have presented an algorithm that they claim determines whether a number is prime in polynomial time relative to the length of the input number in bits.

In the weeks leading up to the parade, the town frequently gains media attention for its residents setting up folding chairs along the town's main street to stake claim to prime viewing areas.

Announcing the death of Life, Maxwell declared: “ We cannot claim, like Mr. Gene Tunney, that we resigned our championship undefeated in our prime.

However, both the prime minister and president stated that Lebanon does have a claim to the area.

" Although the book makes the claim that PAZUZU ( like all entities listed therein ) was of Sumerian origin, critics John Wisdom Gonce III and Daniel Harms document the erroneous nature of such a claim, stating: " Likewise, the demon Pazuzu does not appear in myth until Assyria's rise in the first millennium B. c., long after Sumer's prime ...

The claim that the Progress party is populist dates back to a motion of no confidence in 1986 for the Conservative Party prime minister Kåre Willoch.

As such, a user who uses Prime95 to discover a qualifying prime number would not be able to claim the prize directly.

He was later to claim in a letter written to General Aguiyi Ironsi in 1966, how he had been approached in the Calabar Prison by emissaries of the government a number of times and asked to among others dismantle his own Action Group in exchange for his release and a deputy prime minister's position-an offer he refused

Obote's rivals for leadership within the UPC, supported by some Baganda politicians and others who were hostile to Obote, used the evidence revealed by Amin's casual bank deposit to claim that the prime minister and his closest associates were corrupt and had conducted secret foreign policy for personal gain, in the amount of £ 25, 000 each.

In the Rhine Crisis of 1840, French prime minister Adolphe Thiers advanced the claim that the Upper and Middle Rhine River should serve as his country's " natural eastern border ".

:" he was able to lay immediate claim to prime construction sites at Sheikh Abd el Qurna and Deir el Bahri itself for the excavation of his tomb chapel and burial chamber.

He is involved in the 1988 Malaysian Constitution crisis which the then prime minister Mahathir Mohammad used his killing of an innocent caddy with a golf club as a leverage to hijack the Malaysian judiciary system by sacking the then Lord of President of the Federal Court of Malaysia ( Now known as Chief Justice of Malaysia ), Tun Haji Mohamed Salleh bin Abas in an effort to claim his political success.

This left Antigonus in prime position to claim overall rule over the Macedonian empire.

Many researchers claim that because of the Kennedys ' obsession with getting Castro, Attorney General Robert Kennedy, though angry about the CIA's use of one of his prime Mafia targets, chose to continue these efforts until the Cuban Missile Crisis in October, 1962.

His discovery of the 6th, that corresponding to p = 17 in the formula M < sub > p </ sub >= 2 < sup > p </ sup >- 1, exploded a many-times repeated number-theoretical myth ( Until Cataldi, 19 authors going back to Nicomachus are reported to have made the claim in L. E. Dickson's History of the Theory of Numbers — with a few more repeating this afterward ) that the perfect numbers had units digits that invariably alternated between 6 and 8 ; and that of the 7th ( for p = 19 ) held the record for the largest known prime for almost two centuries, until Leonhard Euler discovered that 2 < sup > 31 </ sup >-1 was the eighth Mersenne prime.

Though by the laws of the Russian Empire, he was the prime claimant after the execution of Tsar and his family by the Bolsheviks, his claim to the throne was met with opposition because at his birth his mother was a Lutheran and not yet a member of the Russian Orthodox Church.

For these reasons some claim that U. S. government pressure was a major factor in the dismissal of Whitlam as prime minister by the governor general, Sir John Kerr, who according to Boyce was referred to as our man Kerr by CIA officers.

The Belgian prime minister Leterme rejected this claim, as the treaty had not yet been ratified by the Wallonian subgovernment.

Janion acquired a building in a prime location on the Honolulu Harbor after the firm of Ladd & Co. went out of business, and some of the last undeveloped land that was part of the claim of former British Consul Richard Charlton.

Mitchell was initially questioned as a witness but was eventually arrested and charged with the crime some 10 months later following months of media speculation, including the repeated claim that the then 15-year-old was the " only " or " prime " suspect.

According to the late John Aspinall, a silverback gorilla in his prime has the physical strength of 7 – 8 Olympic weight lifters but this claim is unverified.