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The multiplicity of a prime which does not divide n may be called 0 or may be considered undefined. Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1.
2.40 Pell primes. 2.41 Permutable ... write the prime factorization of n in base 10 and concatenate the factors; iterate until a prime is reached. 2, 3, 211, 5, 23, 7 ...
The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of 5 ...
In number theory, the prime omega functions and () count the number of prime factors of a natural number . Thereby ω ( n ) {\displaystyle \omega (n)} (little omega) counts each distinct prime factor, whereas the related function Ω ( n ) {\displaystyle \Omega (n)} (big omega) counts the total number of prime factors of n , {\displaystyle n ...
40 is an abundant number.. Swiss mathematician Leonhard Euler noted 40 prime numbers generated by the quadratic polynomial + +, with values =,,,...,.These forty prime numbers are the same prime numbers that are generated using the polynomial + with values of from 1 through 40, and are also known in this context as Euler's "lucky" numbers.
The numbers which remain prime under cyclic shifts of digits. A016114: Home prime: 1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ... For n ≥ 2, a(n) is the prime that is finally reached when you start with n, concatenate its prime factors (A037276) and repeat until a prime is reached; a(n) = −1 if no prime is ever reached. A037274
The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the PrimePages and by Henri & Renaud Lifchitz's PRP Records. Numbers with more than 2,000,000 digits are shown.
A Gaussian integer is either the zero, one of the four units (±1, ±i), a Gaussian prime or composite.The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime.