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 *p*_{n} denotes the *n*th prime number, *O* is big O notation, and "log" is the natural logarithm. This conjecture has not been proven or disproven.

Read more about Cramér's Conjecture: Heuristic Justification, Proven Results On Prime Gaps, Cramér–Granville Conjecture

### 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

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**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:

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—Laurence Sterne (1713–1768)