Kevin Ryde > Math-NumSeq-71 > Math::NumSeq::GoldbachCount

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Module Version: 71   Source   Latest Release: Math-NumSeq-72

# 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,

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

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),

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

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`.

http://user42.tuxfamily.org/math-numseq/index.html