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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

What is the biggest Prime Number you can get by arranging consecutive prime numbers side by side? Few examples:

P1=2

P2=23

P3=2357

P4=2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199211223227229233239241251257263269271277281283293307311313317331337347349353359367373379383389397401409419421431433439443449457461463467479487491499503509521523541547557563569571577587593599601607613617619631641643647653659661673677683691701709719 (355 Digits) Hope I didn't miss any prime number in this sequence!

Can you get P5?

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

Just found P5 (499 Digits).

P5=2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199211223227229233239241251257263269271277281283293307311313317331337347349353359367373379383389397401409419421431433439443449457461463467479487491499503509521523541547557563569571577587593599601607613617619631641643647653659661673677683691701709719727733739743751757761769773787797809811821823827829839853857859863877881883887907911919929937941947953967971977983991997100910131019102110311033

So, can someone find P6?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

How do you know there aren't any in between? Have you checked them all?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

I did check them all but in case I missed any one of them, hope people can update it.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

What did you use for checking?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

You can check them using ECPP http://www.ellipsa.eu/ (Primo) or ECM/SIQS/Rabin-Miller http://www.alpertron.com.ar/ECM.HTM

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

Ok, I will see what I can do. How are you doing with finding P6?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

I think P6 would be having 800-1000 digits or even bigger. Would try finding it tomorrow.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

Ok, see you then.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Hi;

P6 = 2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199211223227229233239241251257263269271277281283293307311313317331337347349353359367373379383389397401409419421431433439443449457461463467479487491499503509521523541547557563569571577587593599601607613617619631641643647653659661673677683691701709719727733739743751757761769773787797809811821823827829839853857859863877881883887907911919929937941947953967971977983991997100910131019102110311033103910491051106110631069108710911093109711031109111711231129115111531163117111811187119312011213121712231229123112371249125912771279128312891291129713011303130713191321132713611367137313811399140914231427142914331439144714511453145914711481148314871489149314991511152315311543154915531559156715711579158315971601160716091613161916211627163716571663166716691693169716991709172117231733174117471753175917771783178717891801181118231831184718611867187118731877187918891901190719131931193319491951197319791987199319971999200320112017202720292039205320632069208120832087208920992111211321292131213721412143215321612179220322072213222122372239224322512267226922732281228722932297

It has 1171 digits!

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

Kool Bobbyn:)..then P7 could be at least 2000-3000 Digits..I guess

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

If you need it I can get it.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

P7=235711131719232931374143475359616771737983899710110310710911312713113713914915115716316717317918119119319719921122322722923323924125125726326927127728128329330731131331733133734734935335936737337938338939740140941942143143343944344945746146346747948749149950350952152354154755756356957157758759359960160761361761963164164364765365966167367768369170170971972773373974375175776176977378779780981182182382782983985385785986387788188388790791191992993794194795396797197798399199710091013101910211031103310391049105110611063106910871091109310971103

11091117112311291151115311631171118111871193120112131217122312291231123712491259127712791283128912911297130113031307131913211327136113671373138113991409142314271429143314391447145114531459147114811483148714891493149915111523153115431549155315591567157115791583159716011607160916131619162116271637165716631667166916931697169917091721172317331741174717531759177717831787178918011811182318311847186118671871187318771879188919011907191319311933194919511973197919871993199719992003201120172027202920392053

20632069208120832087208920992111211321292131213721412143215321612179220322072213222122372239224322512267226922732281228722932297230923112333233923412347235123572371237723812383238923932399241124172423243724412447245924672473247725032521253125392543254925512557257925912593260926172621263326472657265926632671267726832687268926932699270727112713271927292731274127492753276727772789279127972801280328192833283728432851285728612879288728972903290929172927293929532957296329692971299930013011301930233037

This number has 1543 Digits, ok Bobby, get me P8.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

P8=2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199211223227229233239241251257263269271277281283293307311313317331337347349353359367373379383389397401409419421431433439443449457461463467479487491499503509521523541547557563569571577587593599601607613617619631641643647653659661673677683691701709719727733739743751757761769773787797809811821823827829839853857859863877881883887907911919929937941947953967971977983991997100910131019102110311033103910491051106110631069108710911093109711031109111711231129115111531163117111811187119312011213121712231229123112371249125912771279128312891291129713011303130713191321132713611367137313811399140914231427142914331439144714511453145914711481148314871489149314991511152315311543154915531559156715711579158315971601160716091613161916211627163716571663166716691693169716991709172117231733174117471753175917771783178717891801181118231831184718611867187118731877187918891901190719131931193319491951197319791987199319971999200320112017202720292039205320632069208120832087208920992111211321292131213721412143215321612179220322072213222122372239224322512267226922732281228722932297230923112333233923412347235123572371237723812383238923932399241124172423243724412447245924672473247725032521253125392543254925512557257925912593260926172621263326472657265926632671267726832687268926932699270727112713271927292731274127492753276727772789279127972801280328192833283728432851285728612879288728972903290929172927293929532957296329692971299930013011301930233037304130493061306730793083308931093119312131373163316731693181318731913203320932173221322932513253325732593271329933013307331333193323332933313343334733593361337133733389339134073413343334493457346134633467346934913499351135173527352935333539354135473557355935713581358335933607361336173623363136373643365936713673367736913697370137093719372737333739376137673769377937933797380338213823383338473851385338633877388138893907391139173919392339293931394339473967398940014003400740134019402140274049405140574073407940914093409941114127412941334139415341574159417742014211421742194229423142414243425342594261427142734283428942974327433743394349435743634373439143974409442144234441444744514457446344814483449345074513451745194523454745494561456745834591459746034621463746394643464946514657466346734679469147034721472347294733475147594783478747894793479948014813481748314861487148774889490349094919493149334937494349514957496749694973498749934999500350095011502150235039505150595077508150875099510151075113511951475153516751715179518951975209522752315233523752615273527952815297530353095323533353475351538153875393539954075413541754195431543754415443544954715477547954835501550355075519552155275531555755635569557355815591562356395641564756515653565756595669568356895693570157115717573757415743574957795783579158015807581358215827583958435849585158575861586758695879588158975903592359275939595359815987600760116029603760436047605360676073607960896091610161136121613161336143615161636173619761996203621162176221622962476257626362696271627762876299630163116317632363296337634363536359636163676373637963896397642164276449645164696473648164916521652965476551655365636569657165776581659966076619663766536659666166736679668966916701670367096719673367376761676367796781679167936803682368276829683368416857686368696871688368996907691169176947694969596961696769716977698369916997700170137019702770397043705770697079710371097121712771297151715971777187719372077211721372197229723772437247725372837297730773097321733173337349735173697393741174177433745174577459747774817487748974997507751775237529753775417547754975597561757375777583758975917603760776217639764376497669767376817687769176997703771777237727774177537757775977897793781778237829784178537867787378777879788379017907791979277933793779497951796379938009801180178039805380598069808180878089809381018111811781238147816181678171817981918209821982218231823382378243826382698273828782918293829783118317832983538363836983778387838984198423842984318443844784618467850185138521852785378539854385638573858185978599860986238627862986418647866386698677868186898693869987078713871987318737874187478753876187798783880388078819882188318837883988498861886388678887889389238929893389418951896389698971899990019007901190139029904190439049905990679091910391099127913391379151915791619173918191879199920392099221922792399241925792779281928392939311931993239337934193439349937193779391939794039413941994219431943394379439946194639467947394799491949795119521953395399547955195879601961396199623962996319643964996619677967996899697971997219733973997439749976797699781978797919803981198179829983398399851985798599871988398879901990799239929993199419949996799731000710009100371003910061100671006910079100911009310099101031011110133101391014110151101591016310169101771018110193102111022310243102471025310259102671027110273102891030110303103131032110331103331033710343103571036910391103991042710429104331045310457104591046310477104871049910501105131052910531105591056710589105971060110607106131062710631106391065110657106631066710687106911070910711107231072910733107391075310771107811078910799108311083710847108531085910861108671088310889108911090310909109371093910949109571097310979109871099311003110271104711057110591106911071110831108711093111131111711119111311114911159111611117111173111771119711213112391124311251112571126111273112791128711299113111131711321113291135111353113691138311393113991141111423114371144311447114671147111483114891149111497115031151911527115491155111579115871159311597116171162111633116571167711681116891169911701117171171911731117431177711779117831178911801118071181311821118271183111833118391186311867118871189711903119091192311927

5719 digits!

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

Hi anonimnystefy!

Can you get us P9?:)

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

Maybe, if you gave me enough time.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

You will need a lot of time. P(9) has more than 121444 digits.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

It's not fair!

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Why is it not fair? It is a lot better to know something about the size of problem you are given. Then you know whether or not to try it.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

It is not fair because the next one is so large. I wanted to find one myself. Now I can't.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

You could have found it.

**In mathematics, you don't understand things. You just get used to them.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

Don't give up anonimnystefy! The largest Prime nearly 13 million digits! 100k digits is not that big in comparison.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

No one knows what P(9) is, the 100000+ digits is only a lower bound. It could be much more.

To verify the primality of each number takes a long time even using the fastest algorithms.

**In mathematics, you don't understand things. You just get used to them.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 201

I agree bobbym, sometimes the next prime just jumps into gigantic number out of blue. Sometimes they are just next to each other. You can never understand prime.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Hi;

Generally the primes thin out. It is natural to expect in this case that there would be big jumps each time.

**In mathematics, you don't understand things. You just get used to them.**

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