primeness

简明释义

英[ˈpraɪmnəs]美[ˈpraɪmnəs]

n. 初期；主要；基本

英英释义

单词用法

同义词

反义词

例句

1.You can't tell for certain that a number is prime without trying to factor it, but you can apply a number of simpler tests that will verify its primeness to any degree of certainty that you want.

你不能没有试着分解某个数就肯定地说这个数是质数，但是你可以使用大量的简单测试在某种你需要的程度上确认它是质数。

2.Finite automaton, a computational model of extremely limited computing ability, was proved to have the capability of solving primeness test by construction.

有穷自动机，一种计算能力极其有限的计算模型，具有解决素性测试的能力通过构造法得到了证明。

3.You can't tell for certain that a number is prime without trying to factor it, but you can apply a number of simpler tests that will verify its primeness to any degree of certainty that you want.

你不能没有试着分解某个数就肯定地说这个数是质数，但是你可以使用大量的简单测试在某种你需要的程度上确认它是质数。

4.In Chapter 5, we study how the co-primeness of element orders of a finite group influences its structure.

第五章主要研究有限群中元素的阶的互素性对群结构的影响。

5.The teacher explained how to determine the primeness of a number using various methods.

老师解释了如何使用各种方法来确定一个数字的primeness。

6.When studying prime factors, understanding primeness helps simplify complex problems.

在研究质因数时，理解primeness有助于简化复杂问题。

7.The software program checks for the primeness of numbers to optimize performance in calculations.

该软件程序检查数字的primeness以优化计算性能。

8.In cryptography, the primeness of numbers is essential for creating secure encryption algorithms.

在密码学中，数字的primeness对于创建安全的加密算法至关重要。

9.The mathematician was fascinated by the concept of primeness because it plays a crucial role in number theory.

这位数学家对primeness的概念着迷，因为它在数论中扮演着关键角色。

作文

In the realm of mathematics, the concept of prime numbers has always held a special place. Prime numbers are those greater than one that have no positive divisors other than one and themselves. The beauty of these numbers lies not only in their simplicity but also in their complexity. When we delve deeper into the world of prime numbers, we encounter the idea of primeness, which refers to the quality or state of being prime. This characteristic is essential for various applications in number theory, cryptography, and even computer science.Understanding primeness requires us to explore the fundamental properties of prime numbers. For instance, the number two is the smallest and the only even prime number. All other even numbers can be divided by two, thereby disqualifying them from being prime. This uniqueness of two sets the stage for our understanding of primeness. As we progress through the sequence of numbers, we find that primes become increasingly sparse, yet they remain infinitely numerous. This paradox highlights the intriguing nature of primeness in mathematics.One of the most fascinating aspects of primeness is its role in the field of cryptography. Modern encryption methods often rely on the difficulty of factoring large composite numbers into their prime factors. For instance, the RSA algorithm, widely used for secure data transmission, hinges on the primeness of certain large numbers. The security of this method relies on the fact that while multiplying two large primes is computationally feasible, breaking down the product back into its prime components is extraordinarily challenging. This application underscores how the concept of primeness extends beyond theoretical mathematics and finds practical significance in our digital lives.Moreover, the study of primeness has led to many unsolved problems and conjectures in mathematics. One such example is the Goldbach Conjecture, which posits that every even integer greater than two can be expressed as the sum of two prime numbers. Despite extensive numerical evidence supporting this conjecture, a formal proof remains elusive. This ongoing quest to understand primeness reflects the dynamic nature of mathematical inquiry, where each discovery leads to new questions and challenges.In addition to its mathematical implications, primeness can also serve as a metaphor in various aspects of life. Just as prime numbers are indivisible, individuals who embody the qualities of primeness can be seen as those who maintain their integrity and uniqueness in a world that often encourages conformity. Embracing one's primeness allows for personal growth and authenticity, fostering a sense of individuality that is crucial in today’s society.In conclusion, the concept of primeness is not merely an abstract idea confined to the pages of mathematics textbooks. It permeates various fields, from cryptography to philosophical discussions about individuality. As we continue to explore the depths of primeness, we uncover not only the fundamental truths of mathematics but also valuable insights into the human experience. Whether we are calculating prime factors or reflecting on our own uniqueness, the essence of primeness remains a vital part of our understanding of the world around us.

在数学领域，素数的概念一直占据着特殊的位置。素数是指大于一的数，只有一个和它本身两个正因数。这些数字的美丽不仅在于它们的简单性，也在于它们的复杂性。当我们深入探讨素数的世界时，我们会遇到“primeness”这个概念，它指的是作为素数的特质或状态。这一特性对于数论、密码学乃至计算机科学的各种应用至关重要。理解primeness需要我们探索素数的基本特性。例如，数字二是最小的也是唯一的偶素数。所有其他偶数都可以被二整除，从而使它们不符合素数的定义。二的独特性为我们理解primeness奠定了基础。当我们在数字序列中逐步推进时，会发现素数变得越来越稀疏，但它们仍然是无限的。这一悖论突显了数学中primeness的迷人特性。primeness的一个迷人方面是它在密码学领域中的作用。现代加密方法通常依赖于将大型合成数分解为其素因子的困难。例如，RSA算法广泛用于安全数据传输，其基础正是某些大型数字的primeness。该方法的安全性依赖于这样一个事实：虽然将两个大素数相乘是计算上可行的，但将乘积分解回其素因子却极其具有挑战性。这一应用强调了primeness这一概念超越理论数学并在我们的数字生活中找到实际意义。此外，对primeness的研究还导致了许多未解决的问题和猜想。例如，哥德巴赫猜想认为每个大于二的偶整数都可以表示为两个素数的和。尽管有大量数字证据支持这一猜想，但正式证明仍然难以实现。这一持续探索primeness的过程反映了数学研究的动态特性，每一次发现都会引出新的问题和挑战。除了其数学意义外，primeness也可以在生活的各个方面作为隐喻。正如素数是不可分割的，体现primeness特质的个体可以被视为那些在一个常常鼓励同质化的世界中保持诚信和独特性的人。拥抱个人的primeness能够促进个人成长和真实感，这在当今社会中至关重要。总之，primeness的概念不仅仅是一个局限于数学教科书的抽象思想。它渗透到多个领域，从密码学到关于个体性的哲学讨论。随着我们继续探索primeness的深度，我们不仅揭示了数学的基本真理，还获得了对人类经验的宝贵见解。无论我们是在计算素因数还是反思自己的独特性，primeness的本质始终是我们理解周围世界的重要部分。