### 5.1.119 primefactors

`Syntax:`
  `primefactors (` int/bigint/number_expression `)`
  `primefactors (` int/bigint/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 int(s)/bigint(s), no ring needs to be active.
  When called with numbers these are assumed to be integers in a polynomial ring over Q.
  The method finds all prime factors of an integer n. n' will contain the sign, be zero, or the rest (when a bound is given) respectively. The returned list contains the following information: The returned list contains the following information:
  L[1][i] = i-th prime factor (in ascending order),
  L[2][i] = multiplicity of L[1][i],
  L[3] = n'
`Example:`

        bigint n = bigint(7)^12 * bigint(37)^6 * 121;
        primefactors(n);
      ==> [1]:
      ==>    [1]:
      ==>       7
      ==>    [2]:
      ==>       11
      ==>    [3]:
      ==>       37
      ==> [2]:
      ==>    [1]:
      ==>       12
      ==>    [2]:
      ==>       2
      ==>    [3]:
      ==>       6
      ==> [3]:
      ==>    1
        primefactors(n,25);
      ==> [1]:
      ==>    [1]:
      ==>       7
      ==>    [2]:
      ==>       11
      ==> [2]:
      ==>    [1]:
      ==>       12
      ==>    [2]:
      ==>       2
      ==> [3]:
      ==>    2565726409

See prime.

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