Math::NumSeq::AlmostPrimes -- semiprimes and other fixed number of prime factors


 use Math::NumSeq::AlmostPrimes;
 my $seq = Math::NumSeq::AlmostPrimes->new (factor_count => 2);
 my ($i, $value) = $seq->next;


The sequence of numbers having a given number of prime factors. The default is the semiprimes factor_count => 2 giving products of two primes P*Q, which is 4,6,9,10,14,15,etc. For example 15 because 15=3*5.

factor_count => $c controls how many prime factors are to be used. 1 is the primes themselves (the same as Math::NumSeq::Primes). Or for example factor count 4 the sequence is 16,24,36,40,54,60,etc, eg. 60=2*2*3*5.

multiplicity => 'distinct' asks for products of distinct primes. For the default 2 factors this means no squares like 4=2*2, leaving 6,10,14,15,21,etc. For other factor count it eliminates any repeated factors, so for example factor count 4 becomes 210,330,390,462,510,546,etc. The first in the sequence is the primorial 2*3*5*7=210.


See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::AlmostPrimes->new ()

Create and return a new sequence object.

$bool = $seq->pred($value)

Return true if $value is an almost-prime, ie. it has exactly factor_count many prime factors, and if distinct is true then all those factors different.

This check requires factorizing $value and in the current code a hard limit of 2**32 is placed on values to be checked, in the interests of not going into a near-infinite loop.


Math::NumSeq, Math::NumSeq::Primes, Math::NumSeq::PrimeFactorCount




Copyright 2010, 2011, 2012, 2013 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <>.