Math::NumSeq::Primes -- prime numbers
use Math::NumSeq::Primes; my $seq = Math::NumSeq::Primes->new; my ($i, $value) = $seq->next;
The prime numbers, not divisible by anything except themselves and 1.
2, 3, 5, 7, 11, 13, 17, 19, ... (A000040) starting i=1
Currently this is implemented with
Math::Prime::XS generating blocks of primes with a sieve of Eratosthenes. The result is reasonably progressive. On a 32-bit system there's a hard limit at 2^31 (though even approaching that takes a long time to calculate).
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::Primes->new ()
Create and return a new sequence object.
$bool = $seq->pred($value)
Return true if
$valueis a prime.
In the current code a hard limit of 2**32 is placed on the
$valueto be checked, in the interests of not going into a near-infinite loop.
$i = $seq->value_to_i_estimate($value)
Return an estimate of the i corresponding to
$valuecan be any size, it's not limited as in
pred(). See "Value to i Estimate" below.
In the current code the number of count of primes up to value is estimated by the well-known asymptotic
i ~= value/log(value)
Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
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