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Polignac's and conjecture
In 1849 he made Polignac's conjecture:

Polignac's and number
In number theory, de Polignac's formula, named after Alphonse de Polignac, gives the prime decomposition of the factorial n < nowiki >!</ nowiki >, where n ≥ 1 is an integer.

Polignac's and such
There is no mention of such motivation in Polignac's personal memoirs or in the memoirs of the Restoration court.

Polignac's and .
Of her innumerable witty sayings the best known is her remark on the cardinal de Polignac's account of St Denis's miraculous walk of two miles with his head in his hands -- Il n ' y a que le premier pas qui coûte ( The distance doesn't matter ; it is only the first step that is the most difficult.
A year later, his mother's former friend ascended the throne as King Charles X. Polignac's political sympathies did not alter and he was one of the most conspicuous ultra-royalists during the Restoration era.
On 18 March 1830, the liberal majority in the Chamber of Deputies made the Address of the 221 ( motion of no confidence ) against the king and Polignac's ministry.
In addition to Proust and Antonio de La Gandara, the Princesse de Polignac's salon was frequented by Isadora Duncan, Jean Cocteau, Claude Monet, Serge Diaghilev, and Colette.
There's a small disadvantage of the De Polignac's formula is that we need to know all the primes up to n.

conjecture and from
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.
" Alternate History " looks at " what if " scenarios from some of history's most pivotal turning points and presents a completely different version, sometimes based on science and fact, but often based on conjecture.
He picked up another credited Weil conjecture, around 1967, which later under pressure from Serge Lang ( resp.
His attitude towards conjectures was that one should not dignify a guess as a conjecture lightly, and in the Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.
For example, the Riemann hypothesis is a conjecture from number theory that ( amongst other things ) makes predictions about the distribution of prime numbers.
The most celebrated single question in the field, the conjecture known as Fermat's Last Theorem, was solved by Andrew Wiles but using tools from algebraic geometry developed during the last century rather than within number theory where the conjecture was originally formulated.
Woudhuizen revived a conjecture to the effect that the Tyrsenians came from Anatolia, including Lydia, whence they were driven by the Cimmerians in the early Iron Age, 750 – 675 BC, leaving some colonists on Lemnos.
First, an example of M code from 2010, a solution to a benchmarking exercise based on calculating the longest sequence encountered when calculating the longest sequence of the Collatz conjecture for a range of integers.
An example of a theorem from geometric model theory is Hrushovski's proof of the Mordell – Lang conjecture for function fields.
One conjecture holds that " Nazareth " is derived from one of the Hebrew words for ' branch ', namely ne · ṣer, נ ֵ֫ צ ֶ ר, and alludes to the prophetic, messianic words in Book of Isaiah 11: 1, ' from ( Jesse's ) roots a Branch ( netzer ) will bear fruit.
As formal conjecture about real-world issues becomes inextricably linked to automated calculation, information storage and retrieval, such knowledge becomes increasingly " exteriorised " from its knowers in the form of information.
The design claim is often challenged as an argument from ignorance, since it is often unexplained or unsupported, or explained by conjecture.
In this case A is called the hypothesis of the theorem ( note that " hypothesis " here is something very different from a conjecture ) and B the conclusion ( A and B can also be denoted the antecedent and consequent ).
The Collatz conjecture: one way to illustrate its complexity is to extend the iteration from the natural numbers to the complex numbers.
An unproven statement that is believed to be true is called a conjecture ( or sometimes a hypothesis, but with a different meaning from the one discussed above ).
This variation might suggest the early rulers came from a hybrid Anglo-British dynasty or that the rule of early Wessex shifted between more than one royal clan, but this is conjecture.
Scholars conjecture that the red stains on its flanks are not blood but rather the juice from pomegranates, which were a symbol of fertility.
remarked his original ( and not marginal ) conjecture followed from the following statement
It is also known as the " strong ", " even ", or " binary " Goldbach conjecture, to distinguish it from a weaker corollary.
This formula has been rigorously proven to be asymptotically valid for c ≥ 3 from the work of Vinogradov, but is still only a conjecture when.
The cartographic depictions of the southern continent in the 16th and early 17th centuries, as might be expected for a concept based on such abundant conjecture and minimal data, varied wildly from map to map ; in general, the continent shrank as potential locations were reinterpreted.
Scholars conjecture that the type pieces may have been cast from a series of matrices made with a series of individual stroke punches, producing many different versions of the same glyph.

conjecture and 1849
In 1849 de Polignac made the more general conjecture that for every natural number k, there are infinitely many prime pairs p and p such that p p
The conjecture was first made by Ernst Kummer in 1849 December 28 and 1853 April 24 in letters to Leopold Kronecker, reprinted in, and independently rediscovered around 1920 by Philipp Furtwängler and,

conjecture and states
Mathematically, the conjecture states that, for generic initial data, the maximal Cauchy development possesses a complete future null infinity.
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.
< td > The Erdős – Straus conjecture states that, for every positive integer n ≥ 2, there exists a solution in x, y, and z, all as positive integers.
The conjecture states: An equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence: if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it.
This is the content of the twin prime conjecture, which states There are infinitely many primes p such that p + 2 is also prime.
Goldbach's conjecture states that every even integer greater than 2 can be expressed as the sum of two primes.
In mathematics, Tait's conjecture states that " Every 3-connected planar cubic graph has a Hamiltonian cycle ( along the edges ) through all its vertices ".
The conjecture states that this is the only case of two consecutive powers.
the conjecture states that for n > 1.
Goldbach's conjecture states that every even integer greater than 2 can be represented as a sum of two prime numbers.
In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that:
The generalized Poincaré conjecture states that Every simply connected, closed n-manifold is homeomorphic to the n-sphere.
The functoriality conjecture states that a suitable homomorphism of L-groups is expected to give a correspondence between automorphic forms ( in the global case ) or representations ( in the local case ).
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.
In mathematics the modularity theorem ( formerly called the Taniyama – Shimura – Weil conjecture and several related names ) states that elliptic curves over the field of rational numbers are related to modular forms.
Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures.
In mathematics, Lawson's conjecture states that the Clifford torus is the only minimally embedded torus in the 3-sphere S < sup > 3 </ sup >.
William Thurston's elliptization conjecture states that a closed 3-manifold with finite fundamental group is spherical, i. e. has a Riemannian metric of constant positive sectional curvature.
The Geometry and Topology of Three-Manifolds, 1980 Princeton lecture notes on geometric structures on 3-manifolds, that states his elliptization conjecture near the beginning of section 3.
Already in 1955, Jean-Pierre Serre had used the analogy of vector bundles with projective modules to formulate Serre's conjecture, which states that every finitely generated projective module over a polynomial ring is free ; this assertion is correct, but was not settled until 20 years later.
The Robertson conjecture states that if

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