Talk:Legendre sieve

There is a confussion between the "Legendre-Eratosthenes sieve" and the "Legendre-Eratosthenes algorithm" to calculate the number of primes between x and x2. When talking about the sieve, we are referring to the use o linear forms (linearization...aproximations) that are estimates; there we can point out that there is cummulative error due to the fractional parts. When talking about the algorithm, we are referring to a method that uses the floor function and does not accumulate error.

The confussion between the algorithm and the sieve is quite common. Often the word sieve is used instead of algorithm. It is so common that on its own it is not considered an error. The problem appears when both are mixed in the same definition, as is the case in this article of wikipedia. The mathematical description presented, using the floor function, does not produce fractional parts and does not accumulate error. Nonetheless, in the smalll segment called "limitations", it is stated that it accumulates errors due to the fractional part.

If there is a limitation with the algorithm, it is the working time (iterations) it requires as it is only efficient to find the number of primes between x an x2, once the primes less than x have already been identified. Yet, it does not idetinfies the primes (the original sieve of Eratosthenes identifies the primes through an elimination procedure).

You can confirm what I am saying by reading the first two pages of the article Iwaniec that is already given as reference. — Preceding unsigned comment added by 2800:370:89:CD90:31A9:50A:A714:3FC4 (talk) 16:16, 23 December 2018 (UTC)