Whether or not Danchin is correct in suggesting that Thompson's resumption of the opium habit also dates from this period is, of course, a matter of conjecture.

Whether it could be as disastrous for American labor as, say, Jimmy Hoffa of the Teamsters, is a matter of conjecture.

Our conjecture is, then, that regardless of the manner in which school lessons are taught, the compulsive child accentuates those elements of each lesson that aid him in systematizing his work.

Because all clades are represented in the southern hemisphere but many not in the northern hemisphere, it is natural to conjecture that there is a common southern origin to them.

In some applications it is useful to be able to compute the Bernoulli numbers B < sub > 0 </ sub > through B < sub > p − 3 </ sub > modulo p, where p is a prime ; for example to test whether Vandiver's conjecture holds for p, or even just to determine whether p is an irregular prime.

A conjecture is a proposition that is unproven.

In mathematics, a conjecture is an unproven proposition that appears correct.

In mathematics, any number of cases supporting a conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample would immediately bring down the conjecture.

Sometimes a conjecture is called a hypothesis when it is used frequently and repeatedly as an assumption in proofs of other results.

For example, the Riemann hypothesis is a conjecture from number theory that ( amongst other things ) makes predictions about the distribution of prime numbers.

Because many outstanding problems in number theory, such as Goldbach's conjecture are equivalent to solving the halting problem for special programs ( which would basically search for counter-examples and halt if one is found ), knowing enough bits of Chaitin's constant would also imply knowing the answer to these problems.

He is remembered today for Goldbach's conjecture.

Goldbach is most noted for his correspondence with Leibniz, Euler, and Bernoulli, especially in his 1742 letter to Euler stating his Goldbach's conjecture.

In computability theory, the Church – Turing thesis ( also known as the Turing-Church thesis, the Church – Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis ) is a combined hypothesis (" thesis ") about the nature of functions whose values are effectively calculable ; or, in more modern terms, functions whose values are algorithmically computable.

Little is known of his life before he became a bishop ; the assignment of his birth to the year 315 rests on conjecture.

Mathematically, the conjecture states that the maximal Cauchy development of generic compact or asymptotically flat initial data is locally inextendible as a regular Lorentzian manifold.

Whether this formula produces an infinite quantity of Carmichael numbers is an open question ( though it is implied by Dickson's conjecture ).

The conjecture is stated in terms of three positive integers, a, b and c ( whence comes the name ), which have no common factor and satisfy a + b = c. If d denotes the product of the distinct prime factors of abc, the conjecture essentially states that d cannot be much smaller than c.

* The Hadwiger conjecture on the number of strictly smaller homothetic copies of a convex body that may be needed to cover it

* The Hadwiger conjecture in combinatorial geometry concerns the minimum number of smaller copies of a convex body needed to cover the body, or equivalently the minimum number of light sources needed to illuminate the surface of the body ; for instance, in three dimensions, it is known that any convex body can be illuminated by 16 light sources, but Hadwiger's conjecture implies that only eight light sources are always sufficient.

Since ε can be replaced by a smaller value, we can also write the conjecture as, for any positive ε,

* Hadwiger conjecture ( combinatorial geometry ) that for any n-dimensional convex body, at most 2 < sup > n </ sup > smaller homothetic bodies are necessary to contain the original

Harald Cramér conjectured that the gap is always much smaller, ; if Cramér's conjecture is true, Legendre's conjecture would follow for all sufficiently large numbers.

Because the conjecture follows from Andrica's conjecture, it suffices to check that each prime gap starting at p is smaller than A table of maximal prime gaps shows that the conjecture holds to 10 < sup > 18 </ sup >.

For instance, Goldbach's conjecture is the assertion that every even number ( greater than 2 ) is the sum of two prime numbers.

Many questions around prime numbers remain open, such as Goldbach's conjecture, which asserts that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, which says that there are infinitely many pairs of primes whose difference is 2.

By explaining past changes by analogy with present phenomena, a limit is set to conjecture, for there is only one way in which two things are equal, but there are an infinity of ways in which they could be supposed different.

In fact, by assuming the Elliott – Halberstam conjecture or a slightly weaker version, they were able to show that there are infinitely many n such that at least two of n, n + 2, n + 6, n + 8, n + 12, n + 18, or n + 20 are prime.

Goldbach's conjecture states that every even integer greater than 2 can be expressed as the sum of two primes.

Goldbach's third version ( equivalent to the two other versions ) is the form in which the conjecture is usually expressed today.

Statistical considerations which focus on the probabilistic distribution of prime numbers present informal evidence in favour of the conjecture ( in both the weak and strong forms ) for sufficiently large integers: the greater the integer, the more ways there are available for that number to be represented as the sum of two or three other numbers, and the more " likely " it becomes that at least one of these representations consists entirely of primes.

The strong Goldbach conjecture is in fact very similar to the twin prime conjecture, and the two conjectures are believed to be of roughly comparable difficulty.

* The Goldbach conjecture for practical numbers, a prime-like sequence of integers, was stated by Margenstern in 1984, and proved by Melfi in 1996: every even number is a sum of two practical numbers.

Certain principles ( e. g., for any two objects, there is a collection of objects consisting of precisely those two objects ) could be directly seen to be true, but the continuum hypothesis conjecture might prove undecidable just on the basis of such principles.

A well-known conjecture is that the bound ( except for the two knots mentioned ) is 6.

The conjecture states that this is the only case of two consecutive powers.

His thesis proves a conjecture by Edward Witten that two quantum gravitational models are equivalent.

Goldbach's conjecture states that every even integer greater than 2 can be represented as a sum of two prime numbers.

This conjecture has two parts to the hypothesis: the shape must be ' a rectangle ' and ' have four sides of equal length ' and the mathematician would like to know if she can remove either assumption and still maintain the truth of her conjecture.

This conjecture is called " weak " because if Goldbach's strong conjecture ( concerning sums of two primes ) is proven, it would be true.

Given two reductive groups and a ( well behaved ) morphism between their corresponding L-groups, this conjecture relates their automorphic representations in a way that is compatible with their L-functions.

The function obtained in this way is, remarkably, a cusp form of weight two and level N and is also an eigenform ( an eigenvector of all Hecke operators ); this is the Hasse – Weil conjecture, which follows from the modularity theorem.

The Goormaghtigh conjecture says there are only these two cases.

In fact, the elliptization conjecture is logically equivalent to two simpler conjectures: the Poincaré conjecture and the spherical space form conjecture.