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 ).

A prime example of such a claim is the translation of the last line Job speaks ( 42: 6 ), which is extremely problematic in the Hebrew.

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.

Hence the prime issue, as I see it, is whether a democratic or free society can master technology for the benefit of mankind, or whether technology will rule and develop its own society compatible with its own needs as a force of nature.

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.

Whether considered alone or in relation to other editions, COLH 40 is a document of prime importance.

A prime objective of the Army Quartermaster Corps program is to find the reasons for beef's low palatability and means of overcoming it, since it is a major and desirable dietary item.

You get back to the captain and tell him this: Somebody's going to take a shot at the prime minister, and Mahzeer is in on the plot.

Yet for much of the globe, Hollywood is just that -- prime, if not sole, source of knowledge.

While Nicomachus ' algorithm is the same as Euclid's, when the numbers are prime to one another it yields the number " 1 " for their common measure.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

As head of state, Queen Elizabeth II is represented in Antigua and Barbuda by a governor general who acts on the advice of the prime minister and the cabinet.

According to the estimate of a former prime minister, Hrant Bagratian, 55 percent of Armenia's GDP is controlled by 44 families.

( Two is a prime number.

* 1945 – An assassination attempt is made on Japan's prime minister, Kantarō Suzuki.

Encore presentations of Disney Channel Original Movies however, still sometimes air on the channel in prime time on the Saturday and Sunday after its original Friday night debut ( Camp Rock, Dadnapped, Starstruck, and Harriet the Spy: Blog Wars are the only exceptions to this rule ).

Some prime examples of this are present on the tracks " Don't Tell Me You Love Me " and " You Can Still Rock in America ".

Rock Springs Nature Preserve in Lancaster County, PA is a property conserved by the Lancaster County Conservancy that is a prime example of a serpentine barren.

How could the Kambojas who otherwise find so prominent a mention ( 1 ) as independent rulers of a great Mahajanapada per Buddhist texts of 500 BCE ; 2 ) as a very salient Kshatriya tribe in Pāṇini's Ashtadhyayi of 400 BCE ; ( 3 ) as an important self-ruling people in Arthashastra of Kautiliya (~ 300 BCE )– the prime minister of Chandragupta Maurya which authority also glorifies the war horses of the Kamboja to be the foremost among the best breed of the known horses while making no reference whatsoever to the Gandharas or their horses ; and ( 4 ) lastly but not the least, also being so importantly referred to the Shahbazgarhi and Mansehra Rock Edicts of Asoka (~ 250 BCE ) etc – fell out of limelight so abruptly and becoming virtually extinct so suddenly in the intervening period of Alexander's invasion ( 326 BCE ) just 50 – 60 years anterior to king Asoka's reign unless we equate them to same people as the Aspasioi and Assakenoi of the Greek writings?

After noticing his exceptional abilities, Rock, a dictatorial candidate for prime minister, selects Godo to fulfill his agenda and travel into deep space and capture the mystical Phoenix, its blood will manifestly heal the Earth ( and selfishly make Rock prime minister ).

* For a finite field of prime order p, the algebraic closure is a countably infinite field which contains a copy of the field of order p < sup > n </ sup > for each positive integer n ( and is in fact the union of these copies ).

The notations can be combined: and mean that the sum or product is over all prime divisors of n.

and similarly and mean that the sum or product is over all prime powers dividing n.

Two whole numbers m and n are called coprime if their greatest common divisor is 1 ; i. e., if there is no prime number that divides both of them.

Define ν < sub > p </ sub >( n ) as the exponent of the highest power of the prime p that divides n. I. e.

where n > 1 is an integer and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.

In order for Thābit's formula to produce an amicable pair, two consecutive Thabit numbers must be prime ; this severely restricts the possible values of n.

where n > m > 0 are integers and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.

If ( m, n ) is regular and M and N have i and j prime factors respectively, then ( m, n ) is said to be of type ( i, j ).

* A Dedekind domain with finitely many nonzero prime ideals P < sub > 1 </ sub >, ..., P < sub > n </ sub >.

Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:

1 may be inserted without changing the value of n ( e. g. 1000 = 2 < sup > 3 </ sup >× 3 < sup > 0 </ sup >× 5 < sup > 3 </ sup >). In fact, any positive integer can be uniquely represented as an infinite product taken over all the positive prime numbers,

Assume it is true for all numbers less than n. If n is prime, there is nothing more to prove.

* The order, or number of elements, of a finite field is of the form p < sup > n </ sup >, where p is a prime number called the characteristic of the field, and n is a positive integer.

* For every prime number p and positive integer n, there exists a finite field with p < sup > n </ sup > elements.