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5.1.106 primefactors
Syntax:
primefactors ( bigint_expression , [ int_expression ] )
Syntax:
primefactors ( number_expression , [ int_expression ] )
Type:
- list
Purpose:
- returns the prime factorisation up to an optionally given bound, b, on the
prime factors
When called with a bigint, no ring needs to be active.
The method is capable of finding all prime factors <= 2^31 - 1, i.e., it
finds all prime factors <= min(2^31-1, b). The quotient, q, arising by
dividing out all found prime factors will also be returned. More concretely,
a list L with three entries is returned:
L[1] = q,
L[2][i] = i-th prime factor (in ascending order),
L[3][i] = multiplicity of L[2][i].
Example:
| bigint n = bigint(7)^12 * bigint(37)^6 * 121;
primefactors(n);
==> [1]:
==> 4297067688845286336289
==> [2]:
==> [1]:
==> 7
==> [2]:
==> 11
==> [3]:
==> 37
==> [3]:
==> [1]:
==> 12
==> [2]:
==> 2
==> [3]:
==> 6
primefactors(n, 15); /* only prime factors <= 15 */
==> [1]:
==> 4297067688845286336289
==> [2]:
==> [1]:
==> 7
==> [2]:
==> 11
==> [3]:
==> 37
==> [3]:
==> [1]:
==> 12
==> [2]:
==> 2
==> [3]:
==> 6
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See
prime.
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