B002: Prime Numbers and Prime Factor Decomposition

Author(s): K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 15.11.1995
Language: Fortran	Revised:

Subroutine subprogram PRMFCT

• sets the first prime numbers into an array;
• performs the decomposition of a positive number N<10007 into its prime factors:

  

• performs the decomposition of the factorial N! of a positive number N<10007 into its prime factors:

  

Note that this allows in particular to handle quotients of factorials of rather large numbers in an exact way.

Structure:

SUBROUTINE subprogram
User Entry Names: PRMFCT
Files Referenced: Unit 6

Usage:

    CALL PRMFCT(MODE,N,NPRIME,NPOWER,M)

Sets the first n prime numbers into an array.

N

(INTEGER) The number n of prime numbers requested.

NPRIME

(INTEGER) One-dimensional array of length . On exit, NPRIME(j), ( ) contains the j-th prime numbers , where

NPOWER

(INTEGER) One-dimensional array of length . On exit, NPOWER(j), ( ) contains the value 1.

M

(INTEGER) Contains, on exit, the number n.

Performs the decomposition of N ( ) or N! ( ) into its prime factors.

N

(INTEGER) The number N itself ( ) or its factorial ( ) to be decomposed into prime factors.

NPRIME

(INTEGER) One-dimensional array of length . On exit, NPRIME(j), ( ) contains the j-th prime numbers , where .

NPOWER

(INTEGER) One-dimensional array of length . On exit, NPOWER(j), ( ) contains the power corresponding to the prime number .

M

(INTEGER) Contains, on exit, the index defined by and for j>M.

Restrictions:

.
or .

Error handling:

Error B002.1: and and .
Error B002.2: out of range.
In both cases, NPRIME(j) and NPOWER(j), ( ) are set to zero and a message is written on
[4] Unit 6, unless subroutine MTLSET (N002) has been called.