| ||||
|---|---|---|---|---|
| Cardinal | one hundred ninety-two | |||
| Ordinal | 192nd (one hundred ninety-second) | |||
| Factorization | 26 × 3 | |||
| Greek numeral | ΡϞΒ´ | |||
| Roman numeral | CXCII | |||
| Binary | 110000002 | |||
| Ternary | 210103 | |||
| Senary | 5206 | |||
| Octal | 3008 | |||
| Duodecimal | 14012 | |||
| Hexadecimal | C016 | |||
192 (one hundred [and] ninety-two) is the natural number following 191 and preceding 193.
192 has the prime factorization . Because it has so many small prime factors, it is the smallest number with exactly 14 divisors, namely 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192. Because its only prime factors are 2 and 3, it is a 3-smooth number. [1]
192 is a Leyland number of the second kind.
The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "100" means twelve squared, "1000" means twelve cubed, and "0.1" means a twelfth.
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit.
A highly composite number is a positive integer that has more divisors than any smaller positive integer. A related concept is that of a largely composite number, a positive integer that has at least as many divisors as any smaller positive integer. The name can be somewhat misleading, as the first two highly composite numbers are not actually composite numbers; however, all further terms are.
The tables contain the prime factorization of the natural numbers from 1 to 1000.
In mathematics, a Riesel number is an odd natural number k for which is composite for all natural numbers n. In other words, when k is a Riesel number, all members of the following set are composite:
23 (twenty-three) is the natural number following 22 and preceding 24.
61 (sixty-one) is the natural number following 60 and preceding 62.
68 (sixty-eight) is the natural number following 67 and preceding 69. It is an even number.
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009. Sloane is the chairman of the OEIS Foundation.
A unitary perfect number is an integer which is the sum of its positive proper unitary divisors, not including the number itself. Some perfect numbers are not unitary perfect numbers, and some unitary perfect numbers are not ordinary perfect numbers.
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is a number in which every prime factor is at most 7. Therefore, 49 = 72 and 15750 = 2 × 32 × 53 × 7 are both 7-smooth, while 11 and 702 = 2 × 33 × 13 are not 7-smooth. The term seems to have been coined by Leonard Adleman. Smooth numbers are especially important in cryptography, which relies on factorization of integers. 2-smooth numbers are simply the powers of 2, while 5-smooth numbers are also known as regular numbers.
In computational number theory, Williams's p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by Hugh C. Williams in 1982.
191 is the natural number following 190 and preceding 192.
Regular numbers are numbers that evenly divide powers of 60 (or, equivalently, powers of 30). Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. As an example, 602 = 3600 = 48 × 75, so as divisors of a power of 60 both 48 and 75 are regular.
288 is the natural number following 287 and preceding 289. Because 288 = 2 · 12 · 12, it may also be called "two gross" or "two dozen dozen".
A k-rough number, as defined by Finch in 2001 and 2003, is a positive integer whose prime factors are all greater than or equal to k. k-roughness has alternately been defined as requiring all prime factors to strictly exceed k.
40,000 is the natural number that comes after 39,999 and before 40,001. It is the square of 200.
60,000 is the natural number that comes after 59,999 and before 60,001. It is a round number. It is the value of (75025).
In cryptography, Very Smooth Hash (VSH) is a provably secure cryptographic hash function invented in 2005 by Scott Contini, Arjen Lenstra, and Ron Steinfeld. Provably secure means that finding collisions is as difficult as some known hard mathematical problem. Unlike other provably secure collision-resistant hashes, VSH is efficient and usable in practice. Asymptotically, it only requires a single multiplication per log(n) message-bits and uses RSA-type arithmetic. Therefore, VSH can be useful in embedded environments where code space is limited.
