Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Artificial_Intelligence
|
| gptkbp:analyzes |
a grid of numbers
|
| gptkbp:can_be_extended_by |
find primes in a range
|
| gptkbp:designed_by |
gptkb:Eratosthenes
|
| gptkbp:developed_by |
gptkb:ancient_Greece
|
| gptkbp:final_step |
collect unmarked numbers as primes
|
| gptkbp:first_step |
create a list of integers from 2 to n
|
| gptkbp:has_programs |
gptkb:Artificial_Intelligence
|
| gptkbp:historical_event |
gptkb:true
|
| gptkbp:historical_significance |
one of the oldest algorithms for primes
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sieve of Eratosthenes
|
| gptkbp:improves |
trial division
|
| gptkbp:input_output |
a positive integer n
list of prime numbers up to n |
| gptkbp:inspired |
other prime finding algorithms
|
| gptkbp:is_a |
deterministic algorithm
non-recursive algorithm |
| gptkbp:is_applicable_to |
large ranges of numbers
|
| gptkbp:is_based_on |
elimination of multiples
|
| gptkbp:is_considered |
a classic algorithm
a fundamental algorithm in mathematics an efficient algorithm for primes |
| gptkbp:is_described_as |
textbooks on algorithms
|
| gptkbp:is_effective_against |
finding all primes less than 10 million
small to medium ranges of numbers |
| gptkbp:is_implemented_in |
gptkb:educational_programs
software libraries many programming languages |
| gptkbp:is_often_compared_to |
Sieve of Atkin
|
| gptkbp:is_optimized_for |
using a bit array
|
| gptkbp:is_part_of |
mathematical education
algorithmic foundations |
| gptkbp:is_related_to |
combinatorial number theory
mathematical induction |
| gptkbp:is_taught_in |
computer science courses
|
| gptkbp:is_used_by |
gptkb:Mathematician
|
| gptkbp:is_used_in |
gptkb:crypt
mathematical research computer programming competitions finding primes in a probabilistic manner |
| gptkbp:related_to |
number theory
|
| gptkbp:requires |
O(n) space for the list
|
| gptkbp:runs_through |
gptkb:true
|
| gptkbp:second_step |
mark multiples of each prime starting from 2
|
| gptkbp:space_complexity |
O(n)
|
| gptkbp:speed |
naive methods for large n
|
| gptkbp:suitable_for |
real-time applications
very large n without optimizations |
| gptkbp:time_complexity |
O(n log log n)
|
| gptkbp:used_for |
finding prime numbers
|
| gptkbp:bfsParent |
gptkb:Ulam_Spiral
|
| gptkbp:bfsLayer |
7
|