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The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. ... 56: 2 3 ·7 ...
2.56 Safe primes. 2.57 Self primes in ... (or prime) is a natural number ... write the prime factorization of n in base 10 and concatenate the factors; iterate until ...
An Erdős–Woods number, since it is possible to find sequences of 56 consecutive integers such that each inner member shares a factor with either the first or the last member. [ 5 ] The only known number n such that φ( n − 1)σ( n − 1) = φ( n )σ( n ) = φ( n + 1)σ( n + 1) , where φ( m ) is Euler's totient function and σ( n ) is the ...
The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs ... [56] The first five of them are prime, but the ...
Roughly speaking, for a number to be highly composite it has to have prime factors as small as possible, but not too many of the same. ... 56 (3): 448–469.
However, in this case, there is some fortuitous cancellation between the two factors of P n modulo 25, resulting in P 4k −1 ≡ 3 (mod 25). Combined with the fact that P 4 k −1 is a multiple of 8 whenever k > 1 , we have P 4 k −1 ≡ 128 (mod 200) and ends in 128, 328, 528, 728 or 928.
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If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem.