- into
their prime factors. In
abstract algebra,
objects that
behave in a
generalized way like
prime numbers include prime elements and
prime ideals. A natural...
- has no
prime factors and is
neither prime nor composite. Many
properties of a
natural number n can be seen or
directly computed from the
prime factorization...
-
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...
-
multiplicity of the
prime factor 2 is 2,
while the
multiplicity of each of the
prime factors 3 and 5 is 1. Thus, 60 has four
prime factors allowing for multiplicities...
- of the
prime numbers: for each Fn,
choose a
prime factor pn; then the
sequence {pn} is an
infinite sequence of
distinct primes. No
Fermat prime can be...
- The
prime-
factor algorithm (PFA), also
called the Good–Thomas
algorithm (1958/1963), is a fast
Fourier transform (FFT)
algorithm that re-expresses the...
- 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...
- (mod 4). Consequently, in the
prime factorization of a
Mersenne number ( ≥ M2 )
there must be at
least one
prime factor congruent to 3 (mod 4). A basic...
-
prime factor of N must lie
between 108 and 101000. More generally, if all 2ei+1 have a
prime factor in a
given finite set S, then the
smallest prime factor...
-
difficulty of
factoring large numbers into
their prime factors. Carl
Pomerance estimated in 1988 that it
would cost $10
million to
factor a
number with...
