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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. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
25 is a square. It is a square number, being 5 2 = 5 × 5, and hence the third non-unitary square prime of the form p 2.. It is one of two two-digit numbers whose square and higher powers of the number also ends in the same last two digits, e.g., 25 2 = 625; the other is 76.
All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random primes in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.
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 ...
Thus, when + is prime, the first factor in the product becomes one, and the formula ... For example, we can use 25 terms in the series, using the 25 primes less than ...
In number theory, the home prime HP(n) of an integer n greater than 1 is the prime number obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions. The mth intermediate stage in the process of determining HP(n) is designated HPn(m). For instance, HP(10) = 773, as 10 factors as 2×5 yielding HP10(1 ...
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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.