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* 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.

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## Some Related Sentences

Hardy and Littlewood

__Hardy__

**and**

__Littlewood__showed that all sufficiently

**large**numbers are

**the**

**sum**

**of**at most 19 fourth powers

**.**

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**
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**.**

Hardy and listed

Lloyd's

**is**not publicly traded, though some**of**its members are__listed__companies, such**as**Hiscox Ltd, Catlin Group Ltd**and**__Hardy__Underwriting Bermuda Ltd**.**
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__**.****"**Seminole

**"**

**is**

__listed__

**as**one

**of**

**the**Muskogean languages in Hardy's list, but it

**is**generally considered

**a**dialect

**of**Creek, rather than

**a**separate language

**(**

**as**she herself comments

**:**

__Hardy__2005

**:**70 ; see also Mithun 2005

**:**462, Crawford ).

The Orlando Sentinels Gregory

__Hardy____listed__it**as****the**seventh best episode**of****the**show with**a**sports theme**.**

Hardy and their

Stan Laurel

**and**Oliver__Hardy__, who had made**a****number****of**very popular short silent films, used**the**arrival**of**sound to deepen__their__well-formed screen characterizations**and**enhance__their__visual humour,**and**went on to great success in talking films**.**
The most famous

**of**these assertions**is**by**the**History Channel in__their__**"**True Horror**"**series**(**produced by__Hardy__Pictures in 2009**)**which states Aldini specifically**as**one**of****the**sources for Mary Shelley's novel**.**
A tag team match in progress-Jeff

__Hardy__kicks Eddie Fatu | Umaga, while__their__respective partners, Triple H**and**Randy Orton, encourage them**and**reach for**the**tags**.**
The bowlers

**and**other broadly comic aspects**of**__their__personas have reminded modern audiences**of**Laurel**and**__Hardy__, who occasionally played tramps in__their__films**.**
The English author Thomas

__Hardy__used**a**fictionalised Wessex**as****a**setting for many**of**his novels, adopting his friend William Barnes ' term Wessex for__their__home county**of**Dorset**and**its neighbouring counties in**the**south**and**west**of**England**.**
Hirschfeld said that modern film stars were more difficult to depict, that silent film comedians such

**as**Laurel**and**__Hardy__**and**Keaton**"**looked like__their__caricatures ".
*" Magic Act

**"**introduced by Jack Benny, featuring Laurel**and**__Hardy__**as**magicians in**a**comedy skit**(**__their__first appearance in**a**sound feature film**)**
She tells

**the**manager her address-1127 Walnut Avenue-and he hires**the**Laurel**and**__Hardy__Transfer Company to deliver**the**piano in__their__freight wagon**.**
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**.*******The British comedy troupe Monty Python mention Tess

**of**

**the**d ' Urbervilles on

__their__1973 comedy record album Monty Python's Matching Tie

**and**Handkerchief on

**the**track

**"**Novel Writing ", in which Thomas

__Hardy__writes Return

**of**

**the**Native before

**a**live audience

**.**

Originally Morecambe

**and**Wise objected to sharing**a**bed**(**which would become one**of**__their__most popular**and**fondly remembered character traits ), but Braben countered that if it was good enough for Laurel**and**__Hardy__it was surely good enough for Morecambe**and**Wise**.**
Moreover,

__Hardy__deliberately pointed out in his Apology that mathematicians generally do not**"**glory in**the**uselessness**of**__their__work ," but rather – because science can be used for evil**as**well**as**good ends –**"**mathematicians may be justified in rejoicing that there**is**one science at any rate,**and**that__their__own, whose very remoteness from ordinary human activities should keep it gentle**and**clean**.****"**

__Hardy__also rejected

**as**

**a**

**"**delusion

**"**

**the**belief that

**the**difference between pure

**and**applied mathematics had anything to do with

__their__utility

**.**

In

**the**late 1950s**the**Scopitone,**a**visual jukebox, was invented in France**and**short films were produced by many French artists, such**as**Serge Gainsbourg, Françoise__Hardy__, Jacques Brel,**and**Jacques Dutronc to accompany__their__songs**.**
In 1992

**and**1993, Robert Crumb was involved in**a**project by**a**Dutch formation, The Beau Hunks,**and**for both__their__albums**"**The Beau Hunks play**the**original Laurel &__Hardy__music**"**
The 1929 film Berth Marks stars

**the**comedy legends Laurel**and**__Hardy__**as**they attempt to reach Pottsville by train for one**of**__their__booked performances**.**
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**.**

Hardy and I

*****

__Hardy__once told Bertrand Russell

**"**If

__I__could prove by logic that you would die in five minutes,

__I__should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in

**the**proof ".

In

**a**1947 lecture,**the**Danish mathematician Harald Bohr said,**"**To illustrate to what extent__Hardy__**and****Littlewood**in**the**course**of****the**years came to be considered**as****the**leaders**of**recent English mathematical research,__I__may report what an excellent colleague once jokingly said**:**' Nowadays, there are only three really great English mathematicians**:**__Hardy__,**Littlewood**,**and**__Hardy__–**Littlewood****.**
R

**.**H**.**N**(**Dick**)**__Hardy__**:**Beeching-Champion**of****the**Railway**(**1989**)**ISBN 0-7110-1855-3**and**Gerard Fiennes**:**__I__Tried to Run**a**Railway**(**1967**)**ISBN 0-7110-0447-1**.**
On May 27, 1928, Peer had

**the**group travel to**the**Victor Camden, New Jersey studios, where they recorded many**of**what would become**their**signature songs, including**:****"**Meet me by**the**Moonlight Alone ";**"**Keep On**the**Sunny Side ";**"**Can**the**Circle be Unbroken ";**"**Little Darling, Pal**of**Mine ";**"**Forsaken Love ";**"**Anchored in Love ";**"**__I__Ain't Goin ' to Work Tomorrow ";**"**Will You Miss Me When I'm Gone ";**"**Wildwood Flower ";**"**River**of**Jordan ";**"**Chewing Gum ";**and****"**John__Hardy__Was**a**Desperate Little Man ".
He

**is**best known for his radio work, particularly on The News Quiz, I'm Sorry__I__Haven't**a**Clue**and**his long-running series**of**monologues Jeremy__Hardy__Speaks to**the**Nation**.**
:"

__I__do not think that G**.**H**.**__Hardy__was talking nonsense when he insisted that**the**mathematician was discovering rather than creating, nor was it wholly nonsense for Kepler to exult that he was thinking God's thoughts after him**.**
The series featured two other actors, regular I'm sorry

__I__haven't**a**clue panelist Jeremy__Hardy__,**and**Alison Steadman**.**__I__have called it

**"**Slapstick

**"**because it

**is**grotesque, situational poetry -- like

**the**slapstick film comedies, especially those

**of**Laurel

**and**

__Hardy__,

**of**long ago

**.**

After appearing in more than

**a**dozen B-movies,**as**well**as**supporting roles,**as**FBI agent Steve Daniels in**the**espionage series__I__Led Three Lives**and****as**LAPD Sergeant Vince Cavelli in The New Breed, he was offered**the**role**of**Dr**.**Steve__Hardy__on**the**soap opera General Hospital**.**
At Backlash 2009, Jeff

__Hardy__defeated his brother Matt__Hardy__in an**"**__I__Quit**"**match after threatening to jump off**a**ladder onto Matt, which he did after**the**match**.****"**

__Hardy__wrote

**of**

**the**review,

**"**alas ...

**the**Spectator brought down its heaviest leaded pastoral staff on

**the**prematurely happy volumes ...

**the**bitterness

**of**that moment was never forgotten, at that moment

__I__wished

__I__was dead

**.**

__Hardy__wrote in

**a**letter to Edmund Gosse on Dec

**.**10, 1882, “

__I__get most extraordinary criticisms

**of**T

**.**on

**a**T

**.**Eminent critics write & tell me in private that it

**is**

**the**most original thing

__I__have done ... while other eminent critics

**(**

__I__wonder if they are

**the**same

**)**print

**the**most cutting rebukes you can conceive -- show me

**(**to my amazement

**)**that

__I__am quite an immoral person ...”

0.900 seconds.