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Every twin prime pair except ( 3, 5 ) is of the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception of < var > n </ var > = 1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8.

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## Some Related Sentences

Every and prime

Hilbert's example: "

**the**assertion that either there are only finitely many__prime__numbers**or**there are infinitely many "**(**quoted**in**Davis 2000: 97 );**and**Brouwer's: "__Every__mathematical species**is**either finite**or**infinite**.**__Every__completely multiplicative function

**is**a homomorphism

**of**monoids

**and**

**is**completely determined by its restriction to

**the**

__prime__numbers

**.**

* In any ring R

**,**a maximal ideal**is**an ideal M that**is**maximal**in****the**set**of**all proper ideals**of**R**,**i**.**e**.**M**is**contained**in**exactly**2**ideals**of**R**,**namely M itself**and****the**entire ring R**.**__Every__maximal ideal**is****in**fact__prime__**.**__Every__third odd

**number**

**is**divisible by

**3**

**,**which requires that no three successive odd numbers can be

__prime__unless one

**of**them

**is**

**3**

**.**

* 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__**.**__Every__

__prime__ideal P

**in**a Boolean ring R

**is**maximal:

**the**quotient ring R / P

**is**an integral domain

**and**also a Boolean ring

**,**so it

**is**isomorphic to

**the**field F

**<**sub

**>**

**2**

**</**sub >, which shows

**the**maximality

**of**P

**.**Since maximal ideals are always

__prime__

**,**

__prime__ideals

**and**maximal ideals coincide

**in**Boolean rings

**.**

__Every__strong probable

__prime__to base a

**is**also an Euler probable

__prime__to

**the**same base

**,**but not vice versa

**.**

__Every__closed 3-manifold has a

__prime__decomposition: this means it

**is**

**the**connected sum

**of**

__prime__three-manifolds

**(**this decomposition

**is**essentially unique

**except**

**for**a small problem

**in**

**the**case

**of**non-orientable manifolds ).

:

__Every__oriented__prime__closed 3-manifold can be cut along tori**,**so that**the**interior**of**each**of****the**resulting manifolds has a geometric structure**with**finite volume**.**
*

__Every__**number****of****the****form****2****<**sup**>**m**</**sup**>**p**for**a**natural****number**m**and**a__prime__**number**p such that p**<****2****<**sup**>**m**+****1****</**sup**>****is**also semiperfect**.**__Every__group

**of**

__prime__order

**is**cyclic

**,**since Lagrange's theorem implies that

**the**cyclic subgroup generated by

Iwasawa worked

**with**so-called-extensions: infinite extensions**of**a**number**field**with**Galois group isomorphic to**the**additive group**of**p-adic integers**for****some**__prime__p**.**__Every__closed subgroup**of****is****of****the****form****,**so by Galois theory**,**a-extension**is****the**same thing as a tower**of**fields such that**.**__Every__imperfect field

**is**necessarily transcendental over its

__prime__subfield

**(**

**the**minimal subfield ), because

**the**latter

**is**perfect

**.**

A finitely-generated abelian group

**is**indecomposable if**and**only if it**is**isomorphic to Z**or**to a factor group**of****the****form****for****some**__prime__**number**p**and****some**positive integer**n****.**__Every__finitely-generated abelian group**is**a direct sum**of****(**finitely many**)**indecomposable abelian groups**.**
*

__Every__non-split**,**__prime__**,**alternating link that**is**not a torus link**is**hyperbolic by a result**of**William Menasco**.**

Every and pair

__Every__ATM cell has an 8-or 12-bit Virtual Path Identifier

**(**VPI

**)**

**and**16-bit Virtual Channel Identifier

**(**VCI

**)**

__pair__defined

**in**its header

**.**

*

__Every____pair__**of**congruence relations**for**an unknown integer x**,****of****the****form**x ≡ k**(**mod a**)****and**x ≡ l**(**mod b ), has a solution**,**as stated by**the**Chinese remainder theorem ;**in**fact**the**solutions are described by a single congruence relation modulo ab**.**__Every__Saturday night

**,**from 1995 to 2000

**,**he would host a

__pair__

**of**horror films

**(**such as Friday

**the**13th Part

**2**

**and**Wes Craven's New Nightmare

**)**provide a running commentary

**,**trivia

**,**off-color jokes

**and**a drive-in total

**.**

This

__pair__**of**brothers later wrote a book entitled Foot by Foot Through**the**USA**,**A High Adventure Odyssey To__Every__State**in****the**Union**,**which chronicled their journey**.**__Every__constraint

**is**

**in**turn a

__pair__

**(**usually represented as a matrix ), where

**is**an-tuple

**of**variables

**and**

**is**an-ary relation on

**.**

__Every__minimal

__pair__

**of**

**natural**numbers has

**and**

**,**

**for**otherwise

**the**

__pair__would belong to

**and**be at least as small

**in**both coordinates

**,**contradicting

**the**assumption that

**is**minimal

**.**

__Every__

__pair__

**of**MojoNation nodes maintained a relative credit balance

**,**

**with**every EGTP request transferring

**some**Mojo credit from

**the**sender to

**the**receiver

**.**

__Every__

__pair__plays against a

**number**

**of**opposing pairs

**in**successive rounds

**,**depending on

**the**size

**of**

**the**field

**.**

__Every__homeroom

**is**led by a

__pair__

**of**teachers

**with**combined native language abilities

**in**both English

**and**Mandarin

**,**

**and**at every year level

**,**teachers

**of**

**the**two languages collaborate to plan

**and**teach outcomes from

**the**school's inquiry-based integrated program

**.**

Knopfler performed " Money

**for**Nothing " using his Pensa-Suhr signature MK-1 model guitar**with**a__pair__**of**Soldano SLO-100 tube / valve amplifier heads**and**Marshall speaker cabinets during**the**Nelson Mandela 70th Birthday Tribute**and**Prince's Trust concerts**in**1988**,**as well as**the**Nordoff-Robbins charity show at Knebworth**in**1990**and****the**On__Every__Street world tours**in**1991 / 1992**.**__Every__

__pair__

**of**balls

**(**Hamming spheres

**)**are non-intersecting by

**the**t-error-correcting property

**,**

**and**each ball contains

**(**

**in**other words

**,**

**the**volume

**of**

**the**ball

**)**m words

**.**

As described

**in**an article**in****the**London newspaper**,**The Daily Courier**,**on June 25**,**1896: "__Every__one who has watched a bout**with****the**foils knows that**the**task**of**judging**the**hits**is****with**a__pair__**of**amateurs difficult enough**,****and****with**a well-matched__pair__**of**maîtres d ’ escrime well-nigh impossible**.**__Every__convex centrally symmetric polyhedron P

**in**R

**<**sup

**>**

**3**

**</**sup

**>**admits a

__pair__

**of**opposite

**(**antipodal

**)**points

**and**a path

**of**length L joining them

**and**lying on

**the**boundary ∂ P

**of**P

**,**satisfying

__Every__complex

**number**has both a real part

**and**an imaginary part

**,**so one complex variable

**is**two-dimensional

**and**a

__pair__

**of**complex variables

**is**four-dimensional

**.**

Every and except

__Every__member

**of**

**the**future protectionist cabinet then

**in**parliament

**(**

__except__Disraeli

**)**voted against

**the**measure

**.**

__Every__action specifically intended to prevent procreation

**is**forbidden

**,**

__except__

**in**medically necessary circumstances

**.**

__Every__president since Taft

**,**

__except__

**for**Jimmy Carter

**,**threw out at least one ceremonial first ball

**or**pitch

**for**Opening Day

**,**

**the**All-Star Game

**,**

**or**

**the**World Series

**,**usually

**with**much fanfare

**.**

__Every__S / 360

**(**

__except__

**for**

**the**Model 20

**,**which was not a standard S / 360

**)**had a byte-multiplexer channel

**and**

**1**

**or**more selector channels

**.**

__Every__element s

**,**

__except__a possible greatest element

**,**has a unique successor

**(**next element ), namely

**the**least element

**of**

**the**subset

**of**all elements greater than s

**.**

__Every__subset which has an upper bound has a least upper bound

**.**

__Every__album

**,**

__except__1969's The Chicago Transit Authority

**,**1978's Hot Streets

**and**1995's Night

**and**Day: Big-Band

**,**released by Chicago Transit Authority / Chicago has been

**the**band name followed by a Roman numeral

**or**numbered

**in**

**some**other manner

**.**

__Every__state

__except__Nebraska has a bicameral legislature

**,**meaning that

**the**legislature consists

**of**two separate legislative chambers

**or**houses

**.**

__Every__deity

**and**demi-god had been invited

**,**

__except__Eris

**,**

**the**goddess

**of**strife

**(**no one wanted a troublemaker at a wedding ).

__Every__corn-growing country decided to increase tariffs

**in**reaction to this

**,**

__except__Britain

**and**Belgium

**.**

__Every__British North Atlantic route was suspended until 1856

__except__Cunard's Liverpool-Halifax-Boston service

**.**

__Every__evening since 1928

**(**

__except__

**for**a period during

**the**Second World War when Ypres was occupied by Germany ), at precisely eight o ' clock

**,**traffic around

**the**imposing arches

**of**

**the**Menin Gate Memorial has been stopped while

**the**Last Post

**is**sounded beneath

**the**Gate by

**the**local fire brigade

**.**

__Every__sequence

**in**principle has a generating function

**of**each type

**(**

__except__that Lambert

**and**Dirichlet series require indices to start at

**1**rather than

**0**), but

**the**ease

**with**which they can be handled may differ considerably

**.**

__Every__day had

**the**name

**of**an agricultural plant

**,**

__except__

**the**5th

**(**Quintidi

**)**

**and**10th day

**(**Decadi

**)**

**of**every decade

**,**which had

**the**name

**of**a domestic animal

**(**Quintidi

**)**

**or**an agricultural tool

**(**Decadi ).

__Every__episode

__except__one featured a live performance by a band

**,**including Madness

**,**Motörhead

**,**

**and**The Damned

**.**

__Every__state

**,**

__except__Arkansas

**and**Mississippi

**,**maintains a state FEPA

**(**see EEOC

**and**state FEPA directory ).

__Every__day had

**the**name

**of**an agricultural plant

**,**

__except__

**the**5th

**(**Quintidi

**)**

**and**10th day

**(**Decadi

**)**

**of**every decade

**,**which had

**the**name

**of**a domestic animal

**or**an agricultural tool

**,**respectively

**.**

__Every__province

**in**Canada

__except__Alberta has either a Provincial Sales Tax

**(**PST

**)**

**or**

**the**Harmonized Sales Tax

**(**HST ), which

**is**a single

**,**blended combination

**of**

**the**GST

**and**PST

**.**

1.123 seconds.