Follow me on Twitter for my latest adventures!

I just found out about Google's Treasure Hunt 2008. They say that "it's a puzzle contest designed to test yer problem-solving skills in computer science, networking, and low-level UNIX trivia."

Apparently I have missed the first three puzzles (first, second and third) but I'll give the fourth puzzle a shot.

The fourth problem is about prime numbers and it's formulated as following:

Find the smallest number that can be expressed as

the sum of 7 consecutive prime numbers,

the sum of 17 consecutive prime numbers,

the sum of 41 consecutive prime numbers,

the sum of 541 consecutive prime numbers,

and is itself a prime number.For example, 41 is the smallest prime number that can be expressed as

the sum of 3 consecutive primes (11 + 13 + 17 = 41) and

the sum of 6 consecutive primes (2 + 3 + 5 + 7 + 11 + 13 = 41).

## The Solution

I'll write how I got the solution as I go, so I'll mix the past and present tenses in this post. Sometimes I'll write what I am going to do and sometimes I'll write what I just did.

I have no desire to generate lists of prime numbers myself as it has been done infinitely many times already. I'll just use a publicly available list of prime numbers! Here is a list of first fifty million primes.

I'll use my Unix-fu to find the solution.

First I noticed that the primes are zipped and split into chunks of million primes per file. The file names are like "primes1.zip", ... "primes50.zip".

A quick loop from 1 to 50 and wget gets all these files to my hard drive:

$ for i in $(seq 50); do wget "http://primes.utm.edu/lists/small/millions/primes$i.zip"; done

Next, I unzip all these files, and remove those zips to save space:

$ for i in $(seq 50); do unzip "primes$i.zip" && rm -f "primes$i.zip"; done

After doing that and looking at what I got, I realized that they were in some strange format, 8 primes per line, space padded and with some text on the first two lines. Here is an example how the first five lines look in primes1.txt file:

The First 1,000,000 Primes (from primes.utm.edu) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89

I want all my primes to be in one file and one prime per line so I can extract N-th prime by looking at that line.

I used the following command to merge all the files into a single file:

for i in $(seq 50); do (awk 'BEGIN { OFS="\n" } NR > 2 {print $1,$2,$3,$4,$5,$6,$7,$8}' primes$i.txt >> primes.txt) && rm -f primes$i.txt; done

A quick verification that I did not lose any primes:

$ wc -l primes.txt 50000000 primes.txt

Now I'll create four files which contain sums of 7, 17, 41 and 541 consecutive primes, not exceeding the biggest prime in primes.txt file. I did that with the following AWK one-liner:

$ last=$(tail -1 primes.txt) $ for N in 7 17 41 541 do awk 'BEGIN { prev[0] = 0 } NR < '$N' {prev[NR] = $1; sum += $1 } NR >= '$N' { psum += prev[NR-'$N']; delete prev[NR-'$N']; prev[NR] = $1; sum += $1; if (sum - psum > '$last') { exit } printf "%d\n", sum - psum }' primes.txt > primes$N.txt done

The command created primes7.txt, primes17.txt, primes 41.txt and primes541.txt files. These files contain sums of prime numbers and just some of them are primes.

The solution, if it exists in the given data set, is the intersect of all these files. If there are multiple items in the intersect, the smallest should be chosen and checked if it really was a prime.

$ sort -nm primes541.txt primes41.txt | uniq -d | sort -nm primes17.txt - | uniq -d | sort -nm primes7.txt - | uniq -d 7830239 $ grep -m1 7830239 primes.txt 7830239

We have found the solution! It's **7830239**!

I submitted the answer and after a few minutes it was confirmed to be correct! Awesome!

Your question: [7, 17, 41, 541]

Your answer: 7830239

Time received: 2008-06-06 23:33:26.268414 UTCCorrect answer: 7830239

Your answer was: Correct

Now leave a comment and tell me how you solved this problem!

## Comments

Fuck, man, awesomely eclectic. I did mine in python and generated the primes (it was computationally less expensive for me to do that than to download them from the net). I then did the same algorithm in python. I'm confident it runs much faster than yours, but I'm also ashamedly confident that it took me a while longer to actually code it.

I was very pleased to find this site.I wanted to thank you for this great read!! I definitely enjoying every little bit of it and I have you bookmarked to check out new stuff you post.

independence day wallpapers

independence day images|

independence day quotes||

independence day sms|

independence day wishes|

independence day poems|

independence day message|

independence day |

Happy independence day images|

Happy independence day quotes|

independence day speech|

independence day greetings|

I really love your blog.I wanted to thank you for this great read!! I definitely enjoying each and every little bit of the article and I have you bookmarked your site to check out new stuff you post.

independence day images

happy independence day images.

When "The Special One" took over Chelsea in 2013 season, he was very much identified weaknesses in the squad m88 London team and immediately found a way to overcome in the shortest time.

The successive shocks which broke out. First, Mourinho wants to bring Manchester United striker Wayne Rooney to Stamford Bridge. Then the attitude and lack of confidence in Fernando Torres M88 as well as Juan Mata actions pushed up the bench. As explained Mourinho, he wants to improve the team with the best quality M88, despite having eliminated the pillars of Chelsea at the moment before he set foot in London.

I really love your blog.I wanted to thank you for this great read!! I definitely enjoying each and every little bit of the article and I have you bookmarked your site to check out new stuff you post.

fiba 2014

fiba world cup

fiba world cup 2014

Basketball world cup 2014

fiba world cup schedule

fiba world cup 2014 teams

fiba world cup 2014 groups

fiba live streaming,

Good Lord you were lucky; I got 5, 25, 343, and 1017. Not sure what I was on, but I did binary lookups for the 1017s and the brute-forced the successes to check 5, 25, and 343. We can call it the Crack Algorithm&tm;, respecting what I must've been on to ignore all the possible optimizations.

Still, you get 41 and 541, and I get 343 and 1017. Sometimes life's just no fair.

Treasure Design MLB New York Yankees – Solid Distressed for LeNu Samsung Galaxy S3 I9300 3D Best Durable Case

MagicSky Plastic Silicone Armored Hybrid Polka Dot Pattern Case for Apple iPhone 4 4S 4G – 1 Pack – Retail Packaging – Purple

Nokia X2-02 Wallet Pink Clutch Carrying Cover Case with Built-In Credit Card Slots and Detachable Handstrap + NuVur ™ Keychain (ESAMWLP1)

Nokia X2-02 Wallet Pink Clutch Carrying Cover Case with Built-In Credit Card Slots and Detachable Handstrap + NuVur ™ Keychain (ESAMWLP1)

nice ..i also though of doing in shell script first but then it became messy. Then i did it in c, though procedure is same.

I'm also writing to let you be aware of what a excellent discovery my friend's princess gained checking the blog. <A>electrical store

I'm also writing to let you be aware of what a excellent discovery my friend's princess gained checking the blog. <A>electrical store

I wish i know how to use shell in that way!

:D

I did my solution in F#. but im pretty sure it was pure brute force.

Apple iPhone 5 5G 5S Be Free Birds Cute Quote Retro Vintage WHITE Sides Slim HARD Case Skin Cover Protector Accessory Vintage Retro Unique AT&T Sprint Verizon Virgin Mobile

I did a simple python script that used binary search to find the wanted sums, I'm pretty sure it's faster.

Jeez, that must have taken a long time. I decided to do it with a sample of about 5 million or so primes and that took a long time.

Also, btw, why do you need to keep the psum? As far as I can see you are outputing the sum up to that point minus the sum up the the point i primes before that. Just keep the sum minus the prime number i primes ago.

sum += $1 - prev[NR-'$i']; prev[NR] = $1; delete prev[NR-'$i']; print sum

also, why do you quit when the sum is greater than the last prime? Wouldn't that skip the prime numbers at the end of the list? In your case it's ok since the answer comes out WAY before the end of the list, but from the looks of it it would miss the solution if it was at the end of the primes.txt file.

Ian, true, I could have summed it that way.

I quit when the sum is greater than the last prime because I wouldn't be able to verify if the sum was a prime (I don't want to write any verification algorithms myself. I just want to use that primes.txt list).

And you are right about primes at the end of the list, this wouldn't find it. You'd need a bigger prime list 450 million primes.

I did it in perl - and not terribly efficiently. Generated the primes up to 30,000,000 because that's about all that the simple sieve code I found would do in the 4Gb of memory I had available, figured it was probably enough.

And keeping ALL the lists in memory as both arrays and hashes was actually not too bad - wrote it in about 10 minutes and it took another 5 to run. Woot.

My first-pass recursive attempt at the robots thing was totally intractable, and the second time when I forgot to "use bigint" I actually submitted the wrong number through doing insufficient checking (oh the embarassment) - but once you figure that: value(N, M) == value(N - 1, M) + value (N, M - 1) and value (1, x) == value (y, 1) == 1, then it's pretty trivial to just build an N x M array and calculate the values.

It is nice having a multi-core modern machine with 4Gb of ram for the prime problem though - it makes brute force much cheaper, and coming up with a good algorithm for a once-off computation rather worthless.

Looks like a nice showcase for Python's stream-processing approach via generators and other iterators/itertools/etc. Here's the relevant snippet from the itoo.py in my personal toolbox:

[of course there are several other parts of itoo.py but I've picked only the ones used in the following]. Now, using these tools I keep lying around, I wrote uit.py:

Of course, it IS only a Macbook Air, so a faster machine would get better times than 15 seconds!-) But, 15 seconds IS about the additional time it took to write uit.py, and I'd say that's about par for the course.

Alex

Thanks for your excellent comment, Alex! Great usage of Python.

with windows platform? can u tell me how it could be done without shell

Here's my solution in Ruby.

That was really great unix-fu. I used it solve the 4th puzzle, thanks.

One suggestion though - I don't think you need to download all the fifty million prime numbers. I used your code to download just the first zip file, and it worked. My maximum number in the conditionals was 707.

IMO downloading 50 million prime numbers is just wasting computer power :)

Anyway, thanks once again!

llcoolj, you'd need CygWin. It's a linux environment for Windows. Once you install it, you'll be able to use all these commands from cygwin shell.

I used more or less the same approach as you to sum the primes, up to using awk and "delete a[NR-41]". :-) I used "tr -s" instead to split the files to one prime per line. And I used "fgrep -xf" to compute the intersections of the files, which is probably slower than sorting and using uniq.

My solutions:

http://leonardo-m.livejournal.com/63888.html

http://leonardo-m.livejournal.com/64165.html

The faster Python version requires 1 second, the faster D version runs in 0.07 seconds or so.

actually my summing code is the same as Ian's.

I used Python to solve this:

http://kourge.net/node/116

The need to write code for doing list intersections was a bit ugly; if I were using Ruby it wouldn't have needed an "intersection" function because consecutives.inject(:"&") would have done the job, although I'm not sure if Ruby's built-in & method is efficient enough.

My implementation runs about 7 seconds for five conditions. ([3, 5, 143, 865, 1089] => [5990183])

Nice work! I solved this question using similar methods of scripting to you, but utilizing MySQL when performing the sums. Created a 2 column table where I was running the query:

Had to create an index on column 'p' to speed up the summation of the primes (very slow otherwise!). In the end, once the actual table had been created and indexed by MySQL, the solution popped out in a few more minutes of PHP and BASH script.

Ended up with 4 text files, containing all possible potential numbers. Then used a final bit of scripting piped through ‘less’ to manually locate the final answer:

And there’s the answer: 8429539 (for problem 5, 11, 775 and 1151).

And this was all done on a small ITX Linux box with 384Mb of RAM running a VIA Nehemiah 1Ghz cpu. Who needs fast processors and gigs of RAM to solve this!! :-)

Great! Thanks for the detailed explanantion. However, I am not familiar with awk, so will appreciate, if you can explain the following:

1. awk 'BEGIN { OFS="\n" } NR > 2 {print $1,$2,$3,$4,$5,$6,$7,$8}'

2. awk 'BEGIN { prev[0] = 0 } NR = '$N' { psum += prev[NR-'$N'];

Beautiful approach towards solving the problem. I solved the problem using C. Apart from the language advantage, I think my idea is also a little different.

http://ciju.wordpress.com/2008/06/03/google-treasure-hunt/

Guys, you are talking about brute force approach.

I mean these scripts are okay, but google could give us a different task to sum REALLY BIG primes?

How about summing 2^1001+1, 2^31+1?

Who thought about that?

Without math or a brilliant idea, its just a practice of typing code in your favorite programming language, isn't it?

I think about math approach because number of primes in each sum is usually also prime. That could be a google hint to us...

Runnig: I could not agree more with you. However, Quote -->"number of primes in each sum is usually also prime. That could be a google hint to us ".

Well I am not sure about this since I got 2 of my numbers as non prime.( and same seems to be the case with "K" above who got 25 and 343.

But hell you are right(about the (brilliant idea || math)-whatever you may want to call it). There is more information in the question, than any of the provided solutions here, have explioted.

Has anyone used the fact that the solution sets needs to be of necessarily continious prime numbers.

There is more there than meets the eye !

Great! Very inventive approach, imho. I am not fluent in shell-scripting, so for me your article was some kind of demonstration of its power if used sensibly.

I think I found a nice solution: quick and with a low memory footprint

http://mauro.netsons.org/th08.py

Okay. Runnig, as been already siand is undoubtly right. My first thought here was "such a hot lad," second was chaotic and worthless, but begun vomiting keywords such as: erdos, partition function, generatingfunctionology, ergodic theory. Goolge has to generate questions that have answers and all your methods are inefficient. Neverthell the point of this puzzle surely isn't mathematics, its too hard for undergraduate, too easy or pointless for a phd (too lazy to look up references). Therefore it isn't also a programmer's puzzle, because without aforementioned mathematics cannot be solved memory-efficiently. Peteris got it right showing ideal qualifications for a Site Reliability Engineer (uber sysop) at Google. Hot lad.

Please follow the link for more exciting facts about prime

http://kadiprimality.blogspot.com/

I think its perfect. But my opinion is still you need to think on your comment.

I've written mine in D using atkin sieve and it goes about 1s :)

http://dsource.org/projects/tango/wiki/BitArrayVsArrayOfBoolsExample

But solution of a friend of mine beat me to the ground even more than yours.

He wrote it in Haskell in 12 line (including coments and blank lines!) which after some shrinking (but still readable though) went down to 4 iirc :) I'm not sure weather his solution is available online.

Hi,

I solved this fourth problem of Google Treasure Hunt 2008 in very easy way. I just write a C program to give the required output. By this program you can solve for the numbers upto 2^31.(upto any 10 digit number). I submited answers for so many problems of this kind. I got the confirmation for the first problem that I solved.

Find the smallest number that can be expressed as

the sum of 15 consecutive prime numbers,

the sum of 37 consecutive prime numbers,

the sum of 369 consecutive prime numbers,

the sum of 1015 consecutive prime numbers,

and is itself a prime number.

Could you please provide me the answer

I am a good boy and your friend.

Well, I learned about the treasurehunt too late, but I had fun solving these puzzles.

I have bruteforced prime numbers puzzle by generating prime numbers and their sums into the file, and then just grep-ped numbers :)

I did this in Perl first, but I had not enough patience to wait for it, so I've rewritten it in C.

It took about a half an hour to me to solve this :)

Plz help me in doing this problem.

the problem is

n^2-n+41 represent the prime number where n belongs to Natural number.which option is correct for this statement.

(a) n

I got the same answer! But my way, I think was way easier. I just went to the bottom of your post and looked at the answer.

These puzzles remind me of Jon Bentley's "Programming Pearls" columns/books.

nice

bihar board result 2014

thank

nice

bihar board result 2014

thank

nice ..i also though of doing in shell script first but then it became messy

Nice tips

fathers day wishes

happy fathers day wishes

fathers day sms

happy fathers day smsquotes on fathers day

fathers day quotes

Thanks

fathers day quotes

father's day quotes

happy fathers day quotes

fathers day quotes from daughter

fathers day messages

fathers day 2014 Quotes

Fathers Day quotes

fathers day quotes

father's day quotes

happy fathers day quotes

fathers day quotes from daughter

fathers day messages

fathers day 2014 Quotes

Fathers Day Quotes

happy fathers day messages

fathers day greetings messages

Fathers day Messages from Daughter

fathers day sms

fathers day messages in hindi

happy fathers day Quotes from daughter

Happy Father Day Messages

fathers day messages

happy fathers day messages

fathers day messages

father's day messages

fathers day messages from daughter

happy fathers day messages 2014

fathers day

Ramadan Wallpaper

Ramadan Wallpaper HD Download

Ramadan Wallpaper 2014

Ramadan Wallpaper 2014 Download

Ramadan Wallpaper 2014 HD Images

Ramadan Wallpaper 2014 Images

Ramadan Wallpaper quotes

Ramadan wallpaper greetings

Ramadan wallpaper 2014 greetings

Ramadan Wallpaper 2014 quotes

Ramadan Kareem 2014 images

Ramadan Kareem Mubarak Images

Ramadan Kareem Mubarak 2014 images

Ramadan Screen Saver 2014 download

Ramadan Mubarak images

Ramadan images 2014

Ramadan Mubarak greetings

Wish you happy Ramadan 2014

Happy Ramadan Wallpaper 2014

Ramadan wallpaper 2014

Wish you happy Ramadan 2014

ramadan Hd wallpaper 2014

Wish you happy Ramadan wallpaper 2014

Ramadan 2014 images

Ramadan 2014 pictures

wish you happy Ramadan 2014 images

Wish you happy Ramadan 2014 pictures

Happy ramadan 2014 wallpaper

Ramadan Kareem 2014 Wallpaper

Ramadan Mubarak 2014 wallpaper

Wallpaper Ramadan 2014

Ramadan HD wallpaper

Ramadan 2014 HD wallpaper

wish you Ramadan 2014 HD wallpaper

Happy Ramadan HD wallpaper

Happy Ramadan 2014 HD wallpaper

Wish you Ramadan HD wallpaper Download 2014

Ramadan HD wallpaper Download 2014

Ramadan HD wallpaper 2014 Download

Ramadan HD wallpaper 1080p

Ramadan 2014 HD wallpaper 1080p

Best Ramadan 2014 HD wallpaper

Top 10 Ramadan 2014 HD wallpaper

Best Collections Of Ramadan 2014 HD wallpaper

Ramadan 2014 HD wallpaper For Android

Ramadan 2014 best Screensaver download

Ramadan 2014 Screensaver download

screensaver download for mobile Ramadan 2014

Ramadan 2014 HD Screensaver Download

Ramadan 2014 download best screen saver

Screensaver for 2014 ramadan

Ramadan mubarak screensaver download

Ramadan mubarak 2014 best screen saver

Ramadan Kareem Mubarak 2014 best screen saver

Ramadan mubarak 2014 best screen saver

screen saver 2014 download free for android

Ramadan Kareem Mubarak Greetings 2014

Best Collections of Ramadan 2014 Greetings

Best Collections of Ramadan 2014 Greetings

Top Collections of Ramadan 2014 Greetings

Ramadan 2014 Greetings

Ramadan 2014 Greetings Free

Ramadan 2014 Greetings Kareem best

Best Collections of Ramadan 2014 Kareem Greetings

Best Collections of Ramadan 2014 Kareem Greetings

Best Collections of Ramadan 2014 kareem greetings

Top Ramadan 2014 wallpapers

Top Ramadan 2014 pictures

Top ramadan 2014 pictures for pc

Top ramadan 2014 Wallpaper for Android

Ramadan 2014 best softwares

Ramadan 2014 Best Images of Desktop

Ramadan 2014 best pictures for desktop

ramadan 2014 collection of Hd wallpaper

Ramadan 2014 Best collections

Ramadan 2014 top Hd wallpaper

Ramadan 2014 in uk

When Ramadan 2014 in Uk

ramadan 2014 in United Kingdom

When Ramadan 2014 in United States

When ramadan 2014 in America

Ramadan date in uk

Ramadan date in uk

Ramadan facts in united kingdom

Ramadan date in France

Ramadan 2014 in france

Ramadan 2014 date in france

Ramadan 2014 date in Frace country

Happy Ramadan 2014 best wallpaper

Ramadan Wallpaper best collections

Ramadan Kareem Wallpaper collections

wish you happy Ramadan wallpaper 2014

happy Ramadan wallpaper 2014

wish you happy Ramadan Hd wallpaper

Happy Ramadan 2014 HD wallpaper

Hd Ramadan wallpaper 2014

Wallpaper 2014 Hd in Ramadan

Ramadan wallpaper 2014 for Desktop Background

Best Islamic Ramadan wallpaper 2014

Wallpaper 2014 for facebook Cover

Best Wallpaper 2014 Download

Ramadan HD wallpaper 2014 Download

When ramadan in India 2014

Ramadan in India 2014

Ramadan in India 2014

Ramadan Kareem Greetings

Ramadan kareem Mubarak Greetings

Ramadan kareeem 2014 Greetings

Ramadan 2014 kareem Greetings

Ramadan 2014 kareem greetings

Ramadan Kareem Mubarak 2014

Ramadan kareem Mubarak 2014

Ramadan kareem Mubarak 2014

Ramadan Kareem greetings 2014

Ramadan Kareem greetings 2014

Ramadan Kareem greetings 2014

Ramadan Kareem greetings 2014

Ramadan Kareem greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Ramadan Mubarak Greetings 2014

Inspirational pictures of ramadan 2014

Inspirational pictures of ramadan 2014

Inspirational pictures of ramadan 2014

Inspirational pictures of ramadan 2014

Inspirational pictures of ramadan 2014

Inspirational pictures of ramadan 2014

Inspirational pictures of ramadan 2014

Inspirational pictures of ramadan 2014

Inspirational pictures of ramadan 2014

Inspirational pictures of ramadan 2014

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Ramadan 2014 Wallpaper and Mubarak pics

Awesome Post Ramadan Wallpaper Ramadan Wallpaper HD Download Ramadan Wallpaper 2014 Ramadan Wallpaper 2014 Download Ramadan Wallpaper 2014 HD Images Ramadan Wallpaper 2014 Images Ramadan Wallpaper quotes Ramadan wallpaper greetings Ramadan wallpaper 2014 greetings Ramadan Wallpaper 2014 quotes Ramadan Kareem 2014 images Ramadan Kareem Mubarak Images Ramadan Kareem Mubarak 2014 images Ramadan Screen Saver 2014 download Ramadan Mubarak images Ramadan images 2014 Ramadan Mubarak greetings Wish you happy Ramadan 2014 Happy Ramadan Wallpaper 2014 Ramadan wallpaper 2014 Wish you happy Ramadan 2014 ramadan Hd wallpaper 2014 Wish you happy Ramadan wallpaper 2014 Ramadan 2014 images Ramadan 2014 pictures wish you happy Ramadan 2014 images Wish you happy Ramadan 2014 pictures Happy ramadan 2014 wallpaper Ramadan Kareem 2014 Wallpaper Ramadan Mubarak 2014 wallpaper Wallpaper Ramadan 2014 Ramadan HD wallpaper Ramadan 2014 HD wallpaper wish you Ramadan 2014 HD wallpaper Happy Ramadan HD wallpaper Happy Ramadan 2014 HD wallpaper Wish you Ramadan HD wallpaper Download 2014 Ramadan HD wallpaper Download 2014 Ramadan HD wallpaper 2014 Download Ramadan HD wallpaper 1080p Ramadan 2014 HD wallpaper 1080p Best Ramadan 2014 HD wallpaper Top 10 Ramadan 2014 HD wallpaper Best Collections Of Ramadan 2014 HD wallpaper Ramadan 2014 HD wallpaper For Android Ramadan 2014 best Screensaver download Ramadan 2014 Screensaver download screensaver download for mobile Ramadan 2014 Ramadan 2014 HD Screensaver Download Ramadan 2014 download best screen saver Screensaver for 2014 ramadan Ramadan mubarak screensaver download Ramadan mubarak 2014 best screen saver Ramadan Kareem Mubarak 2014 best screen saver Ramadan mubarak 2014 best screen saver screen saver 2014 download free for android Ramadan Kareem Mubarak Greetings 2014 Best Collections of Ramadan 2014 Greetings Best Collections of Ramadan 2014 Greetings Top Collections of Ramadan 2014 Greetings Ramadan 2014 Greetings Ramadan 2014 Greetings Free Ramadan 2014 Greetings Kareem best Best Collections of Ramadan 2014 Kareem Greetings Best Collections of Ramadan 2014 Kareem Greetings Best Collections of Ramadan 2014 kareem greetings Top Ramadan 2014 wallpapers Top Ramadan 2014 pictures Top ramadan 2014 pictures for pc Top ramadan 2014 Wallpaper for Android Ramadan 2014 best softwares Ramadan 2014 Best Images of Desktop Ramadan 2014 best pictures for desktop ramadan 2014 collection of Hd wallpaper Ramadan 2014 Best collections Ramadan 2014 top Hd wallpaper Ramadan 2014 in uk When Ramadan 2014 in Uk ramadan 2014 in United Kingdom When Ramadan 2014 in United States When ramadan 2014 in America Ramadan date in uk Ramadan date in uk Ramadan facts in united kingdom Ramadan date in France Ramadan 2014 in france Ramadan 2014 date in france Ramadan 2014 date in Frace country Happy Ramadan 2014 best wallpaper Ramadan Wallpaper best collections Ramadan Kareem Wallpaper collections wish you happy Ramadan wallpaper 2014 happy Ramadan wallpaper 2014 wish you happy Ramadan Hd wallpaper Happy Ramadan 2014 HD wallpaper Hd Ramadan wallpaper 2014 Wallpaper 2014 Hd in Ramadan Ramadan wallpaper 2014 for Desktop Background Best Islamic Ramadan wallpaper 2014 Wallpaper 2014 for facebook Cover Best Wallpaper 2014 Download Ramadan HD wallpaper 2014 Download When ramadan in India 2014 Ramadan in India 2014 Ramadan in India 2014 Ramadan Kareem Greetings Ramadan kareem Mubarak Greetings Ramadan kareeem 2014 Greetings Ramadan 2014 kareem Greetings Ramadan 2014 kareem greetings Ramadan Kareem Mubarak 2014 Ramadan kareem Mubarak 2014 Ramadan kareem Mubarak 2014 Ramadan Kareem greetings 2014 Ramadan Kareem greetings 2014 Ramadan Kareem greetings 2014 Ramadan Kareem greetings 2014 Ramadan Kareem greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Ramadan Mubarak Greetings 2014 Inspirational pictures of ramadan 2014 Inspirational pictures of ramadan 2014 Inspirational pictures of ramadan 2014 Inspirational pictures of ramadan 2014 Inspirational pictures of ramadan 2014 Inspirational pictures of ramadan 2014 Inspirational pictures of ramadan 2014 Inspirational pictures of ramadan 2014 Inspirational pictures of ramadan 2014 Inspirational pictures of ramadan 2014 Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics Ramadan 2014 Wallpaper and Mubarak pics oHack Anna University Paper Valuation Anna University result 2014 Thanks for sharing

Happy Friendship Day 2014 Greeting cards.

Happy Friendship Day Celebration 2014 messages,poems,greetings,quotes .

Happy FriendShip Day Ideas Gifts For Friends.

Happy Friendship Day English poems Messages Quotes quotes whatsapp wechat facebook hike viber .

thanx

Hey its great post really enjoyed this one i found this on google ,i think there are still websmasters who provide quality contents to the reader and hope to come back soon and by the way Eid Mubarak Wishes

Eid Mubarak Sms in Hindi

Eid Mubarak sms In English

Eid Mubarak sms in Urdu

Eid Mubarak Wallpapers

Eid Mubarak Greetings

Eid Mubarak cardsto all of you also you can check Happy eid Mubarak 2014

really a great stuff

EID Mubarak 2014

Happy EID Mubarak 2014

EID Mubarak Wishes

EID Mubarak Greetings

EID Mubarak 2014

EID Mubarak Wishes 2014

EID Mubarak 2014

EID Mubarak Greetings 2014

EID Mubarak 2014

EID Mubarak SMS

EID Mubarak 2014

EID Mubarak Wallpapers

EID Mubarak 2014

EID Mubarak SMS 2014

EID Mubarak 2014

EID Mubarak Wallpapers 2014

EID Mubarak 2014

EID Wallpapers 2014

EID Mubarak 2014

EID Mubarak Messages 2014 really great stuff

You have a great website. You write realy good stuff on coding. thank you shairng this posts with us.

I think i might come to your blog regularly. Thank you

Meanwhile for all the readers.

Happy Friendship Day SMS

Happy Friendship Day Messages

Friendship Bracelets

Friendship Bands

Happy Friendship Day Cards.

Happy Friendship Day Images

Happy Friendship Day Quotes.

Friendship Day

Happy Friendship Day Facebook Cover.

Happy Friendship Day Ideas

Happy Friendship Day Poems

Happy Friendship Day Shayari

Funny Friendship Day Jokes

Happy Friendship Day Pictures

Happy Friendship Day Wishes

Happy Friendship Day Gifts for Best Friends

Happy Friendship Day Wishes In Punjabi

Advance Friendship Day Wishes SMS

Happy Friendship Day.

Friendship Day 2014.

Friendship Day.

Happy Friendship Day Pinterest Gifts, Images, Pictures, Cards

Happy Festives- Friendship Day 2014 Facebook Pictures

FestCHACHA - Friendship Day 2014 Google Plus

FestCHACHA - Friendship Day Tiwtter

Thank you for giving us the chance to share our thoughts.

Nice article have been published....

raksha bandhan messages

rakhi images

rakhi greeting messages

rakhi cards

rakhi festival

raksha bandhan quotes

rakhi sms

raksha bandhan messages

raksha bandhan messages

raksha bandhan messages

rakhi 2014

raksha bandhan 2014

rakhi sms

raksha bandhan

raksha bandhan 2014

Thanks for sharing.....

Nice Article Have been Published

Independence day Quotes

Happy Independence day Quotes

Independence Day Quotes

Happy Independence Day Quotes

Independence Day Quotes

Happy Independence Day Quotes

Independence Day Quotes

Happy Independence Day Quotes

independence day images

Happy independence day images

Independence day images for whats app

Independence day images

Independence day images

Independence Day Images

Happy Independence Day Images

Thanks for sharing

I am very happy to visit this site and hope to visit here again and again. I have bookmarked your site due to the interesting and relevant stuff found here. Also I have recommended the same to my other friends.

Independence day india

Happy Independence day India

Desh Bhakti songs

Patriotic songs

Whatsapp Status

Fb status

Independence Day Speech in English

Independence Day Quotes

Modi Speech on Independece Day 2014

PM Modi LIVE Speech on Independece Day 2014

This is my site, you can visit it and leave your valuable feedback.

Thank You For Sharing,

Happy Independence Day Images

Independence Day 2014 India

Independence Day Quotes

Independence Day India Wallpapers

Independence Day SMS

Happy Independence Day Wallpapers

Best Independence Day Speeches

Independence Day HD Images

Independence Day 2014

Independence Day Images For Whatsapp

New Independence Day 2014 Quotes

Thanks.

This Article is good and very much useful Teachers day quotes Happy teachers day quotes Teachers day wishes Happy teachers day wishes Teachers day messages Teachers Day SMS Diwali Cards Happy Diwali Cards Diwali Greeting cards Diwali Greetings Happy Diwali Greetings Clt20 Cltt20 2014 Clt20 live streaming Latest Bollywood Movies Box Office Collections Bollywood Movies News Bollywood Movies Reviews Thanks.

Very Nice Sharing

Labor Day 2014

Labor Day Sales 2014.

Get Apple iPhone 6 Price, rumors, specifications, release date and much more Apple iPhone related stuff.

Apple iPhone 6 | Apple iPhone | iPhone 6 | Apple iPhone 6 rumors | iPhone 6 rumors | Apple iPhone 6 release date | iPhone 6 release date | Apple iPhone 6 updates | iPhone 6 updates | Apple iPhone 6 news | iPhone 6 news | Apple iPhone 6 specifications | iPhone 6 specifications | iPhone 6 competition | iPhone 6 leaks | Apple iPhone 6 leaks

Apple iPhone 6 rumors | iPhone 6 rumors | What to expect from the brand new Apple iPhone 6 | What specifications will Apple iPhone 6 have | Apple iPhone 6 release date | iPhone 6 release date | new iPhone release date | When is new iPhone launching | When is Apple iPhone 6 launching | Apple iPhone 6 competition | iPhone 6 competition | iPhone 6 rumors | Apple iPhone 6 leaks | iPhone 6 leaks | Apple iPhone 6 pics | iPhone 6 pics | Apple iPhone 6 Price | iPhone 6 Price | Apple iPhone 6 price in India | iPhone 6 price in India | iPhone 6 price leaked

Thanks for Sharing.

This article is quite helpful and informative too. I enjoyed a lot. Thanks for sharing such a great article.

Amazon Promotional Code 2014

Amazon Promotional Code

Amazon Promotional Code for August 2014

Thanks for sharing such a great article

## Leave a new comment