Assertion: sieve | /r/CapableOf | generate composite
Facets:
value: from its prime factors
type: OTHER
value: directly
type: MANNER
Source sentences:
text: It is not the sieve of Eratosthenes but is often confused with it, even though the sieve of Eratosthenes directly generates the composites instead of testing for them.
text: When testing each prime, the optimal trial division algorithm uses all prime numbers not exceeding its square root, whereas the sieve of Eratosthenes produces each composite from its prime factors only, and gets the primes "for free", between the composites.
text: It is not the sieve of Eratosthenes but is often confused with it, even though the sieve of Eratosthenes directly generates the composites instead of testing for them.
text: When testing each prime, the optimal trial division algorithm uses all prime numbers not exceeding its square root, whereas the sieve of Eratosthenes produces each composite from its prime factors only, and gets the primes "for free", between the composites.