| 词汇 | example_english_prime-number |
| 释义 | Examples of prime numberThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. For this reason, we introduce the environment by considering a tiny demonstration program - a program to compute the nth primenumber. The target was immediately preceded by a masked primenumber, which could be also either larger or smaller than five. The method of proof of both theorems follows the lines of the error term result for the primenumber theorem in analytic number theory. Which primenumber do you want? What is a primenumber? It is not a primenumber, so there are no problems there. From the Hansard archive Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0 For example, one important problem is whether a number is a primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In this example, the main document spawns a web worker to compute prime numbers, and progressively displays the most recently found primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Any number either is prime or is measured by some primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A "primenumber" is defined as a counting number that is divisible only by itself and 1. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Equivalently, a primenumber is a positive integer which has exactly two positive factors: 1 and itself. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A simple example is that almost all prime numbers are odd, which is based on the fact that all but one primenumber are odd. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. For example, it's commonly accepted that the sun is made of gas, on one hand, and that 3 is a primenumber, on the other. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Following this convention, modulo a primenumber there are an equal number of residues and nonresidues. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. For some time it was thought that certain theorems, like the primenumber theorem, could only be proved using higher mathematics. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. If "n" is a primenumber, the algorithm will always return "prime": since "n" is prime, steps 1 and 3 will never return "composite". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. We can also find expressions which relate to prime numbers and the primenumber theorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A palindromic prime is a palindromic number that is a primenumber, for example, 191 and 313. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Computers use base 2, which is a primenumber, so division always works. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. An odd primenumber is congruent to either 1 or 3 modulo 4, and the second possibility has just been ruled out. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Finite fields only exist when the order (size) is a prime power (where is a primenumber and is a positive integer). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Without establishing a specific primenumber, this proves that one exists that is greater than "n", contrary to the original postulate. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Thus, polite non-trapezoidal numbers must have the form of a power of two multiplied by a primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This result has been superseded by the primenumber theorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Usually, a text based on natural numbers (for example, the article primenumber) does not specify the used definition of natural numbers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The lcm will be the product of multiplying the highest power of each primenumber together. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. He also made major investigations in the areas of gamma functions, modular forms, divergent series, hypergeometric series and primenumber theory. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Peano arithmetic is adequate for a good deal of number theory, including the notion of primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The primenumber theorem gives a general description of how the primes are distributed amongst the positive integers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This was the largest known primenumber for 75 years, and the largest ever calculated by hand. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This is to say that it is a primenumber which is one less than a power of two. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The only factorial that is also a primenumber is 2, but there are many primes of the form "n"! 1, called factorial primes. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. All prime numbers are odd, with one exception: the primenumber 2. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A minor modification is needed where a primenumber is repeated. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. When "n" is a primenumber, the prime factorization is just "n" itself, written in bold below. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The primenumber 2 is often considered regular as well. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This is a considerable strengthening of the primenumber theorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. No base 10 pandigital number can be a primenumber if it doesn't have redundant digits. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Another major milestone in the subject is the primenumber theorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The "p" -height considers only divisibility properties by the powers of a fixed primenumber "p". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The classical primenumber theorem serves as a prototypical example, and the emphasis is on abstract asymptotic distribution results. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Proving this doesn't quite require the primenumber theorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It can be shown that the smallest such "n" must be a primenumber, called the "characteristic" of the field. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Here stands for any primenumber different from "p", where "p" is the characteristic of. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Using the primenumber generator provided in the above section, we might define a lazy, but not quite infinite collection. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It will be shown that at least one additional primenumber not in this list exists. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A famous example is the problem of estimating the remainder term in the primenumber theorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This may stand forever as the largest primenumber proven by hand. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. But 137 is a primenumber and not the product of a multiplier and a square. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A finite group is an elementary group if it is "p" -elementary for some primenumber "p". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. They are used in the statement and proof of the primenumber theorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The other adjacent number, 23, is a primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. He traces the primenumber theorem back through history, highlighting the work of some of the greatest mathematical minds along the way. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The problem is that primenumber is a predicate of numbers, not a predicate of human beings. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This gives only two options: either the norm of is a primenumber, or the square of a primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The prime ideals for the integers are the sets that contain all the multiples of a given primenumber, together with the zero ideal. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Thus, there can be no such thing as an ultimate primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The primenumber theorem, proved with techniques from complex analysis, was thought to be a deep result until elementary proofs were found. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The interest of this case was the analogy between the formula obtained, and the explicit formulae of primenumber theory. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This general pattern holds for number fields in general, so that the prime ideal theorem is dominated by the ideals of norm a primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Analytic number theorists are often interested in the error of approximations such as the primenumber theorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In other words, a composite number is any positive integer greater than one that is "not" a primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This was the second-largest known primenumber, and it remained so until 1911. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A repunit prime is a repunit that is also a primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Only repunits (in any base) having a primenumber of digits might be prime. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is the smallest two-digit primenumber in the decimal base; as well as, of course, in undecimal (where it is the smallest two-digit number). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The standard definition of implication allows us to conclude that, since the sun is made of gas, 3 is a primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In primenumber theory, they proved results and some notable conditional results. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A primenumber "q" is a "strong" prime if and both have some large prime factors. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The demand that the characteristic "p" be a primenumber is central to the truth of the freshman's dream. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Each male agent is given a primenumber to identify them. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Leaven hypothesizes that any room marked with a primenumber is a trap. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Given a primenumber that can not be evenly divided into the total sample size. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is also the smallest odd repdigit that is not a primenumber. 33 is the eighth distinct semiprime comprising the prime factors (3 11). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The modern definition of primenumber is positive integer with exactly 2 factors, so 1 is not prime. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Presburger arithmetic can not formalize concepts such as divisibility or primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. However, 7 is the fourth primenumber, and 4 is not prime. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The modulus selected (for both sums) is the primenumber 65,521 (65,535 is divisible by 3, 5, 17 and 257). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. If is a primenumber and divides a product of integers, then divides or divides. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is a primenumber, and a regular prime. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is sufficient to prove the theorem for every odd primenumber "p". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The primenumber theorem says that the average length of the gap between a prime "p" and the next prime is ln "p". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is the unique primenumber with this property. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. We then deduce from this knowledge that there is a primenumber greater than two. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The value of each variable is encoded as the exponent of a primenumber in the prime factorization of the integer. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The primenumber theorem is a key result in this subject. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Any composite number is measured by some primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A natural number greater than 1 that is not a primenumber is called a composite number. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is neither a primenumber nor a composite number. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The number system that results depends on what base is used for the digits: any base is possible, but a primenumber base provides the best mathematical properties. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is the 20th primenumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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