primality

简明释义

英[ˈpraɪməlɪti]美[ˈpraɪməlɪti]

n. 原始；首要；根本；素性

英英释义

单词用法

同义词

反义词

例句

1.Based on some basic theorems in theory of Numbers this program takes advantage of probabilistic algorithm to test a large number for primality.

基于初等数论中的一些基本定理，本程序利用概率算法，快速判定一个大数是否为素数。

2.Prime integers can be efficiently found using a primality test.

使用素数测试可以有效地找到素数整数。

3.Based on some basic theorems in theory of Numbers this program takes advantage of probabilistic algorithm to test a large number for primality.

基于初等数论中的一些基本定理，本程序利用概率算法，快速判定一个大数是否为素数。

4.Of course, much more efficient algorithms for testing primality exist, but this one is the easiest to understand.

当然还有效率更高的素数测试方法，不过这种算法最容易理解。

5.Algorithms that test for primality are widely used in cryptography.

检测素性的算法在密码学中被广泛使用。

6.The concept of primality can be explained through simple examples.

通过简单的例子可以解释素性的概念。

7.The study of primality is essential in number theory.

对素性的研究在数论中至关重要。

8.Mathematicians developed new methods to determine primality more efficiently.

数学家们开发了新的方法来更有效地确定素性。

9.Understanding the primality of large numbers is crucial for secure communications.

理解大数的素性对于安全通信至关重要。

作文

The concept of primality is fundamental in the field of mathematics, particularly in number theory. It refers to the property of a number being prime, which means that it has no positive divisors other than 1 and itself. Understanding primality is crucial for various applications, including cryptography, where prime numbers play a significant role in securing digital communications. In this essay, I will explore the importance of primality, its implications in modern technology, and how mathematicians determine whether a number is prime.To begin with, let us delve deeper into the definition of primality. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. For instance, the numbers 2, 3, 5, 7, and 11 are all prime because they do not have divisors other than 1 and themselves. On the contrary, composite numbers, such as 4, 6, and 8, can be divided by numbers other than 1 and themselves, indicating that their primality is absent.The significance of primality extends beyond theoretical mathematics; it has practical applications in various fields. One of the most notable applications is in the realm of cryptography. Many encryption algorithms, such as RSA, rely on the difficulty of factoring large composite numbers into their prime components. The security of these systems hinges on the properties of primality, making it essential for protecting sensitive information. As technology continues to advance, the demand for secure communication channels increases, further emphasizing the need to understand and utilize primality effectively.Moreover, mathematicians and computer scientists have developed numerous algorithms to test for primality. One of the most famous methods is the Sieve of Eratosthenes, an ancient algorithm that efficiently finds all prime numbers up to a specified integer. More advanced algorithms, such as the Miller-Rabin primality test, allow for the testing of larger numbers, which is particularly useful in cryptographic applications. These algorithms highlight the ongoing research and interest in primality, as mathematicians strive to uncover new methods and improve existing techniques.In addition to its mathematical and technological significance, primality also holds philosophical implications. The study of prime numbers has fascinated mathematicians for centuries, leading to questions about the nature of infinity, the distribution of primes, and their relationship to other mathematical concepts. The enigmatic nature of primality continues to inspire curiosity and exploration within the mathematical community.In conclusion, primality is a vital concept in mathematics with far-reaching implications in technology and philosophy. Its role in cryptography underscores the importance of understanding prime numbers in our increasingly digital world. As we continue to explore the depths of number theory, the study of primality will undoubtedly remain a central focus, driving innovation and enhancing our comprehension of the mathematical universe. Through this exploration, we not only appreciate the beauty of prime numbers but also recognize their significance in securing our future in the digital age.

“primality”这个概念在数学领域，尤其是数论中是基础性的。它指的是一个数是质数的性质，这意味着它除了1和自身之外没有其他正因数。理解primality对于各种应用至关重要，包括密码学，在其中质数在保护数字通信中发挥着重要作用。在这篇文章中，我将探讨primality的重要性，它在现代科技中的影响，以及数学家如何判断一个数是否为质数。首先，让我们更深入地探讨primality的定义。质数被定义为大于1的自然数，无法通过乘以两个较小的自然数来形成。例如，数字2、3、5、7和11都是质数，因为它们没有其他因数，只有1和它们自己。相反，合成数，如4、6和8，可以被1和它们自己以外的数整除，这表明它们缺乏primality。primality的重要性超越了理论数学；它在各个领域有着实际应用。其中最显著的应用之一是在密码学领域。许多加密算法，如RSA，依赖于将大型合成数分解为其质数成分的困难。这些系统的安全性依赖于primality的性质，使得有效理解和利用primality变得至关重要。此外，数学家和计算机科学家开发了众多算法来测试primality。最著名的方法之一是埃拉托斯特尼筛法，这是一种古老的算法，可以有效找到指定整数以下的所有质数。更先进的算法，如米勒-拉宾质数测试，允许对更大的数字进行测试，这在密码学应用中特别有用。这些算法突显了对primality的持续研究和兴趣，因为数学家努力发现新方法并改进现有技术。除了其数学和技术的重要性，primality还具有哲学意义。质数的研究使数学家们着迷几个世纪，引发了关于无限的本质、质数的分布以及它们与其他数学概念之间关系的问题。primality的神秘性质继续激发数学界的好奇心和探索欲。总之，primality是数学中一个重要的概念，对科技和哲学具有深远的影响。它在密码学中的作用强调了理解质数在我们日益数字化的世界中的重要性。随着我们继续探索数论的深度，primality的研究无疑将继续成为中心焦点，推动创新并增强我们对数学宇宙的理解。通过这种探索，我们不仅欣赏质数的美丽，还认识到它们在保护我们数字时代未来中的重要性。