The heap can hold at most ~2B items, which means we can't store
more than this many prime factors.
Note that "fast factors" don't end up in this heap, so the number
of primes we can sieve is actaully the max heap size + the number
of fast factors.
The sieve implementation itself uses a cutoff, so to test primality
of numbers <= K, we need to be able to store prime factors up to
sqrt(K) in our heap. Since our heap can hold ~2B prime factors,
this means the theoretical upper bound on our segmented sieve is
(~2Bth prime)^2.
In practice the sieve will slow down to the point of not being
useful far before we could reach this limit.
Simple heap implementation for storing Factors.
The heap can hold at most ~2B items, which means we can't store more than this many prime factors.
Note that "fast factors" don't end up in this heap, so the number of primes we can sieve is actaully the max heap size + the number of fast factors.
The sieve implementation itself uses a cutoff, so to test primality of numbers <= K, we need to be able to store prime factors up to sqrt(K) in our heap. Since our heap can hold ~2B prime factors, this means the theoretical upper bound on our segmented sieve is (~2Bth prime)^2.
In practice the sieve will slow down to the point of not being useful far before we could reach this limit.