Problems
Unfortunately, the Legendre sieve has a problem with fractional parts of terms accumulating into a large error, which means the sieve only gives very weak bounds in most cases. For this reason it is almost never used in practice, having been superseded by other techniques such as the Brun sieve and Selberg sieve. However, since these more powerful sieves are extensions of the basic ideas of the Legendre sieve, it is useful to first understand how this sieve works.
Read more about this topic: Legendre Sieve
Famous quotes containing the word problems:
“If when a businessman speaks of minority employment, or air pollution, or poverty, he speaks in the language of a certified public accountant analyzing a corporate balance sheet, who is to know that he understands the human problems behind the statistical ones? If the businessman would stop talking like a computer printout or a page from the corporate annual report, other people would stop thinking he had a cash register for a heart. It is as simple as that—but that isn’t simple.”
—Louis B. Lundborg (1906–1981)
“The problems of victory are more agreeable than the problems of defeat, but they are no less difficult.”
—Winston Churchill (1874–1965)
“Currently, U.S. society has been encouraged by its political and subsidized mass-media intelligentsia to view U.S. life as a continual “morning in America” paradise, where the only social problems occur in the inner cities. Psychologists call this denial.”
—Ishmael Reed (b. 1938)