Comments welcome Introduction The openssl command-line binary that ships with the OpenSSL libraries can perform a wide range of cryptographic operations. It can come in handy in scripts or for accomplishing one-time command-line tasks. Documentation for using the openssl application is somewhat scattered, however, so this article aims to provide some practical examples of its use.
See also amicable numbers. Harshad number A Harshad number is a number that is divisible by the sum of its own digits.
Harshad numbers are also known as Niven numbers. A Harshad amicable pair is an amicable pair m, n such that both m and n are Harshad numbers.
There are Harshad amicable pairs in first 5, amicable pairs. Hexadecimal numbers are written using the symbols 0—9 and A—F or a—f. Hexadecimal provides a convenient way to express binary numbers in modern computers in which a byte is almost always defined as containing eight binary digits.
When showing the contents of computer storage — for example, when getting a core dump of storage in order to debug a new computer program or when expressing a string of text characters or a string of binary values — one hexadecimal digit can represent the arrangement of four binary digits.
Two hexadecimal digits can represent eight binary digits, or a byte. For example, the highest common factor hcf of 15 and 17 is 1, since 17 is a prime number. In algebra, the hcf of two or more algebraic expressions may be found by examination of the factors of each: See also large numbers and superfactorials.
Hyperreals emerged in the s from the work of Abraham Robinson who showed how infinitely large and infinitesimal numbers can be rigorously defined and developed in what is called nonstandard analysis.
Hyperreals include all the reals in the technical sense that they form an ordered field containing the reals as a subfield and also contain infinitely many other numbers that are either infinitely large numbers whose absolute value is greater than any positive real number or infinitely small numbers whose absolute value is less than any positive real number.
No infinitely large number exists in the real number system and the only real infinitesimal is zero. But in the hyperreal system, it turns out that that each real number is surrounded by a cloud of hyperreals that are infinitely close to it; the cloud around zero consists of the infinitesimals themselves.
Conversely, every finite hyperreal number x is infinitely close to exactly one real number, which is called its standard part, st x. In other words, there exists one and only one real number st x such that x — st x is infinitesimal.
Integers can be added and subtracted, multiplied, and compared. Like the natural numbers, the integers form a countably infinite set.
An important property of the integers is division with remainder: The numbers q and r are uniquely determined by a and b. From this follows the fundamental theorem of arithmetic, which states that integers can be written as products of prime numbers in an essentially unique way.
The number pifor instance, is far more interesting than 1. Confining our attention to integers, can there be such a thing as an uninteresting number? It is easy to show that the answer must be "no.
Then it must contain a least member, u. But the property of being the smallest uninteresting integer makes u interesting! As soon as u is removed from U, there is a new smallest uninteresting integer, which must then also be excluded.
And so the argument could be continued until U was empty. Given that all integers are interesting can they be ranked from least to most interesting? To be ranked as "least interesting" is an extremely interesting property, and thus leads to another logical contradiction!
When Srinivasa Ramanujanthe great Indian mathematician, was ill with tuberculosis in a London hospital, his colleague G. Hardy went to visit him. Hardy opened the conversation with: That number seems dull to me which I hope isn't a bad omen.The ECM factoring algorithm can be easily parallelized in several machines.
In order to do it, run the factorization in the first computer from curve 1, run it in the second computer from curve , in the third computer from curve , and so on. kcc1 Count to by ones and by tens. kcc2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
kcc3 Write numbers from 0 to Represent a number of objects with a written numeral (with 0 representing a count of no objects). kcc4a When counting objects, say the number names in the standard order, pairing each object with one and only. Prime Numbers. A natural number that possesses only two factors, itself and 1, is called a prime number.
You may think that it would be fairly easy to figure out all of these numbers. Algorithms with numbers iteration of an algorithm, as in several examples later in the chapter.
3. It is the number of bits in the binaryrepresentation of N. European countries. To multiply two decimal numbers xand y, write them next to each other, as in the example below. Then repeat the following: divide the rst number by 2.
I am looking for a memory testing algorithm that will help my team verify the design and test during production (bad soldering, cross-connected address/data lines, mismatched impedances, mirroring etc.).
In any typical programming language course, the student gets a project to write a program that generates prime numbers.
This is considered to be a relatively easy task which is assigned within the first few weeks of the course.