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NAME

Math::NumSeq::GoldbachCount -- number of representations as sum of primes P+Q

SYNOPSIS

use Math::NumSeq::GoldbachCount;
my \$seq = Math::NumSeq::GoldbachCount->new;
my (\$i, \$value) = \$seq->next;

DESCRIPTION

The number of ways each i can be represented as a sum of two primes P+Q, starting from i=1,

# starting i=1
0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, ...

For example i=4 can be represented only as 2+2 so just 1 way. Or i=10 is 3+7 and 5+5 so 2 ways.

Even Numbers

Option on_values => 'even' gives the count on just the even numbers, starting i=1 for number of ways "2" can be expressed (none),

# starting i=1
0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 4, ...

Goldbach's famous conjecture is that for an even i >= 4 there's always at least one P+Q=i, which would be a count here always >= 1.

Odd Numbers

Odd numbers i are not particularly interesting. An odd number can only be i=2+Prime, so the count is simply

count(odd i) = 1  if i-2 prime
0  if not

FUNCTIONS

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

\$seq = Math::NumSeq::GoldbachCount->new ()
\$seq = Math::NumSeq::GoldbachCount->new (on_values => 'even')

Create and return a new sequence object.

Random Access

\$value = \$seq->ith(\$i)

Return the sequence value at \$i, being the number of ways \$i can be represented as a sum of primes P+Q, or with the on_values=>'even' option the number of ways for 2*\$i.

This requires checking all primes up to \$i (or 2*\$i) and the current code has a hard limit of 2**24 in the interests of not going into a near-infinite loop.

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

Return true if \$value occurs as a count. All counts 0 upwards occur so this is simply integer \$value >= 0.