A stronger form of the twin prime conjecture, the Hardy – Littlewood conjecture, postulates a distribution law for twin primes akin to the prime number theorem.

The Hardy – Littlewood conjecture ( after G. H. Hardy and John Littlewood ) is a generalization of the twin prime conjecture.

Pursuing this type of analysis more carefully, Hardy and Littlewood in 1923 conjectured ( as part of their famous Hardy – Littlewood prime tuple conjecture ) that for any fixed c ≥ 2, the number of representations of a large integer n as the sum

* Hardy and Littlewood listed as their Conjecture I: " Every large odd number ( n > 5 ) is the sum of a prime and the double of a prime.

# redirect Twin prime # First Hardy – Littlewood conjecture

This ( along with much else ) led to quantitative progress on the Waring problem, as part of the Hardy – Littlewood circle method, as it became known.

This was a major factor in the development of number theory as a system of conjectures ; examples are the first and second Hardy – Littlewood conjectures.

In a 1947 lecture, the Danish mathematician Harald Bohr reported a colleague as saying, " Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy – Littlewood.

A heuristic estimate ( due to G. H. Hardy and J. E. Littlewood ) for the number of Sophie Germain primes less than n is 2C < sub > 2 </ sub > n / ( ln n )< sup > 2 </ sup > where C < sub > 2 </ sub > is the twin prime constant, approximately 0. 660161.

In 1923, Hardy and Littlewood showed that, assuming the generalized Riemann hypothesis, the odd Goldbach conjecture is true for all sufficiently large odd numbers.

John Edensor Littlewood ( 9 June 1885 – 6 September 1977 ) was a British mathematician, best known for the results achieved in collaboration with G. H. Hardy.

Together they devised the first Hardy – Littlewood conjecture, a strong form of the twin prime conjecture, and the second Hardy – Littlewood conjecture.

With a solid base of young talent assembled over the past five years, including Prince Fielder, Rickie Weeks, J. J. Hardy and Corey Hart, the Brewers showed renewed competitiveness.

* Doordarshan also telecast English cartoons at 12. 00 noon during summer vacations in a programme named " Fun Time " which showed cartoons like Spider-Man, Giant Robo, Gayab Aaya, Guchhae, He-Man and the Masters of the Universe, Jungle Book Shonen Mowgli ( a dubbed Hindi version of a Japanese anime with original music composed by Vishal Bharadwaj ), Talespin & Duck Tales also the comic plays of Charlie Chaplin, Laurel & Hardy and Didi's Comedy Show.

In 2006, BBC Four showed a drama called Stan, based on Laurel meeting Hardy on his deathbed and reminiscing about their career.

When Christian showed up at ringside, Los Conquistadors unmasked themselves, revealing themselves to be Matt Hardy and Jeff Hardy.

Stone Cold showed a new, more vicious side to him as he would attack wrestlers like Brothers of Destruction ( The Undertaker and Kane ), Hardy Boyz ( Matt and Jeff ) and even Lita with the steel chair.

So far these remarks, like most criticisms of Hardy, have tacitly assumed that his poetry is all of a piece, one solid mass of verse expressing a sensibility at a single stage of development.

Alf sed he heard that you and Hardy was a runing together all the time and he though he wod gust quit having any thing mor to doo with you for he thought it was no more yuse.

* L. Hardy, Nonlocality for two particles without inequalities for almost all entangled states.

Strickland and Hardy in 2005 took this argument further, suggesting that the shortbow was a myth and all early English bows were a form of longbow.

" Cryptic was formed as a corporation in California by Jay Clem ( born 1947 ), Homer Flynn ( born April 1945 ), Hardy W. Fox ( born 1945 ), and John Kennedy in 1976, all of whom denied having been band members.

Once Hardy created it, all serial writers used the cliff-hanger even though Anthony Trollope felt that the use of suspense violated " all proper confidence between the author and his reader.

Love Finds Andy Hardy is a 1938 romantic comedy film which tells the story of a teenage boy who becomes entangled with three different girls all at the same time.

While at Roach, McCarey cast Stan Laurel and Oliver Hardy together and guided development of their onscreen characters, thus creating one of the most enduring comedy teams of all time.

Charles Elton ( ecology ), Alister Hardy ( marine biology ) and John Baker ( cytology ) all became highly successful, and Baker eventually wrote Huxley's Royal Society obituary memoir.

Hardy Hempstead ' is still watching over him after all.

While Kenneth R. Hall suggests that Champa was not able to rely on taxes on trade for continuous revenue, but instead financed their rule by raiding neighbouring countries, Hardy argues that the country's prosperity was above all based on commerce.

Apart from Unfinished Dialogue and the 4th edition of Karl Marx, all publications listed from 1978 onwards are compilations or transcripts of various lectures, essays, and letters, edited by Henry Hardy.

George Eliot, Leo Tolstoy, Thomas Hardy, Bolesław Prus, Abraham Cahan, D. H. Lawrence, Machado de Assis, Richard Austin Freeman, and Jorge Luis Borges all referenced Spencer.

In this usage, the recurring personalities adopted by Laurel and Hardy through all of their many comedy films ( despite the fact that they often played characters with different names and professions ) would qualify as their shtick.

Alexandre Hardy ( c. 1570 / 1572 – 1632 ) was a French dramatist, one of the most prolific of all time.

The Syndicate's process for creating the Hardy Boys books consisted of creating a detailed outline, with all elements of plot ; drafting a manuscript ; and editing the manuscript.

The next day, Doricourt, who has been told that Mr. Hardy is on his deathbed, visits him and reluctantly agrees to marry Letitia after all.

Then the disguised Letitia enters and reveals her true identity to the overjoyed Doricourt, who also learns that Hardy was not ill after all.

The current design of the Rangers ' badge was incorporated in 1962, when Ranger Hardy L. Purvis and his mother donated enough Mexican five-peso coins to the DPS to provide badges for all 62 Rangers who were working at that time as commissioned officers.

At the end of the event it was revealed that Nash and Sting had been right about Hogan and Bischoff all along, as they aligned themselves with Jarrett, Abyss and Jeff Hardy.

Authors within this " tradition " were all characterised by a serious or responsible attitude to the moral complexity of life and included Jane Austen, George Eliot, Henry James, Joseph Conrad, and D. H. Lawrence, but excluded Thomas Hardy and Charles Dickens.

Alan toured in cabaret all over the world and performed once with Laurel and Hardy in 1954.

The romance tradition did, however, remain sufficiently powerful to persuade Thomas Hardy, Laurence Binyon and John Masefield to compose Arthurian plays, and T. S. Eliot alludes to the Arthur myth ( but not Arthur ) in his poem The Waste Land, which mentions the Fisher King.

Although he intended to structure the novel into five books, thus mirroring the classical tragic format, Hardy submitted to the tastes of the serial-reading public sufficiently to tack on a happy ending for Diggory Venn and Thomasin in a sixth book, Aftercourses.