Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.

**37** 36 35 34 33 32 **31**

38 **17** 16 15 14 **13** 30

39 18 **5 ** 4 **3** 12 29

40 19 6 1 2 11 28

41 20 **7** 8 9 10 27

42 21 22 23 24 25 26

**43** 44 45 46 47 48 49

It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 = 62%.

If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?

^{?}View Code RSPLUS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | side.length = 1 x <- 1 iter <- 1 ratio = 0.6 isp.n <- 0 N <- 0 while(ratio > 0.1) { last.x <- x[length(x)] side.length <- side.length + 2 x <- rep(last.x,4 ) + c(2,4,6,8)* iter iter <- iter + 1 isp <- gmp::isprime(x) isp.n <- isp.n + sum(as.logical(isp)) N <- N + 4 ratio <- isp.n/N print(side.length) } |

**Answer**: 26241

It's cool that you're participating to Project Euler but please stop posting solutions!

It completely spoils the fun for other people and devalues other players' score, since there's a suspicion that they simply looked up the solution on the internet.

On top of that, those posts appear in R-Bloggers and its subscribers can't avoid them. How would you feel if you were sent the solutions without having had a chance to have a go at a problem?

Hope you understand,

And good luck for the rest of the problems.

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ygc Reply:

May 22nd, 2011 at 1:33 pm

You may noticed that many of the solutions were on the internet.

It is very easy to look up the solution if someone wants to.

Maybe there is some other people who read my post and got to know and participate Project Euler.

At this point of view, what I've done can be a good thing.

Just have fun, don't be so serious.

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lowstz Reply:

May 22nd, 2011 at 3:43 pm

Like the blog title says it：Just for fun~

Readers know it then hack it .

In other way, readers could make a better solutions base on it.

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ygc Reply:

May 22nd, 2011 at 5:15 pm

http://code.google.com/p/projecteuler-solutions/wiki/About

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