In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they can be. It states that
where pn denotes the nth prime number, O is big O notation, and "log" is the natural logarithm. This conjecture has not been proven or disproven.
Other articles related to "conjecture":
... In number theory, and especially the study of diophantine approximation, the lonely runner conjecture is a conjecture originally due to J ... Applications of the conjecture are widespread in mathematics they include view obstruction problems and calculating the chromatic number of distance graphs and circulant graphs ... The conjecture was given its picturesque name by L ...
... Not every conjecture ends up being proven true or false ... The continuum hypothesis, which tries to ascertain the relative cardinality of certain infinite sets, was eventually shown to be undecidable (or independent) from the generally accepted set of axioms of set theory ...
Famous quotes containing the word conjecture:
“What these perplexities of my uncle Toby were,tis impossible for you to guess;Mif you could,I should blush ... as an author; inasmuch as I set no small store by myself upon this very account, that my reader has never yet been able to guess at any thing. And ... if I thought you was able to form the least ... conjecture to yourself, of what was to come in the next page,I would tear it out of my book.”
—Laurence Sterne (17131768)