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NAME

Math::NumSeq::PolignacObstinate -- odd integers not prime+2^k

SYNOPSIS

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

DESCRIPTION

This sequence is integers which cannot be represented as prime+2^k for an integer k. These are counter-examples to a conjecture by Prince de Polignac that every odd integer occurs as prime+2^k (and are called "obstinate" numbers by Andy Edwards).

1, 127, 149, 251, 331, 337, ...

For example 149 is obstinate because it cannot be written as prime+2^k. Working backwards, it can be seen that none of 149-1, 149-2, 149-4, 149-8, ... 149-128 are primes.

A theorem by Erdos gives infinitely many such obstinate integers (in an arithmetic progression).

The value 3 is not in the sequence because it can be written prime+2^k, for prime=2 and k=0.

FUNCTIONS

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

\$seq = Math::NumSeq::PolignacObstinate->new ()

Create and return a new sequence object.

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

Return true if \$value is obstinate, ie. that there's no \$k >= 0 for which \$value - 2**\$k is a prime.

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