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%?

+-%echo
echo(Message,Sender)->Sender ! Message.

+-%prime_list
prime_list()->
	case whereis(primeList) of
		undefined->
			Pid=spawn(euler,prime_list,[initialize]),
			register(primeList, Pid),
			Pid;
		Exists->
			Exists
	end.
prime_list(initialize)->
	put(primes,array:from_list([2,3,5,7,11,13,17,19])),
	put(total,8),
	prime_list(idle);
prime_list(idle)->
	Size=get(total),
	receive
		{get,FromZero,Reply} when FromZero < Size ->
			Reply ! {prime,FromZero,array:get(FromZero,get(primes))};
		{get,FromZero,Reply} ->
			echo({get,FromZero,Reply},self()),
			prime_list(gen);
		{all_below,What,Reply} ->
			case array:get(Size-1,get(primes)) < What of 
				true->
					prime_list(gen),
					echo({all_below,What,Reply},self());
				false->
					Reply ! {primes_below,What,prime_list(below,What,0,[])}
			end;
		{is_prime,What,Reply}->
			Skirt=math:sqrt(What),
			Largest=array:get(Size-1,get(primes)),
			case Largest < What of
				true->
					case Largest < Skirt of 
						true->
							prime_list(gen),
							echo({is_prime,What,Reply},self());
						false->
							Reply ! {is_prime,What,prime_list(check_factors,0,What,Skirt)}
					end;
				false->
					Reply ! {is_prime,What,prime_list(binary_search,What,0,Size-1)}
				end
		end,
		prime_list(idle);
prime_list(gen)->
	Size=get(total),
	Start=array:get(Size-1,get(primes))+2,
	End=Start*10+1,
	Sqrt=math:sqrt(End),
	AsList=array:to_list(get(primes)),
	[2|Odds]=AsList,
	RelevantOdds=lists:takewhile(fun(N)->N =< Sqrt end,Odds),
	Newbs=prime_list(gen,Size,Start,End,RelevantOdds,ordsets:from_list(lists:seq(Start,End,2))),
	put(primes,array:from_list(lists:append(AsList,ordsets:to_list(Newbs)))),
	put(total,get(total)+ordsets:size(Newbs)).
prime_list(check_factors,NextIndex,N,Sqrt)->
	NextPrime=array:get(NextIndex,get(primes)),
	case NextPrime > Sqrt of
		true->true;
		false->
			case N rem NextPrime ==0 of
				true->false;
				false->
					prime_list(check_factors,NextIndex+1,N,Sqrt)
			end
		end;
prime_list(binary_search,What,Low,High) when High-Low < 2 ->
	H=array:get(High,get(primes)),
	L=array:get(Low,get(primes)),
	if
		H == What; L == What ->
			true;
		true->false
	end;
prime_list(binary_search,What,Low,High)->
	Mid=Low+((High-Low) div 2),
	Got=array:get(Mid,get(primes)),
	if
		What > Got->prime_list(binary_search,What,Mid+1,High);
		What < Got->prime_list(binary_search,What,Low,Mid-1);
		true->true
	end;

	
prime_list(below,What,Index,SoFar)->
	Next=array:get(Index,get(primes)),
	if
		Next >= What->
			lists:reverse(SoFar);
		true->
			prime_list(below,What,Index+1,[Next|SoFar])
	end.
prime_list(gen,_,_,_,[],Survivors)->Survivors;
prime_list(gen,Total,Lowest,Highest,[MyPrime|RestPrimes],Survivors)->
	prime_list(gen,Total,Lowest,Highest,RestPrimes,
		ordsets:subtract(Survivors,
			ordsets:from_list(
				lists:seq(Lowest-(Lowest rem MyPrime),Highest,MyPrime)))).

p58()->
	p58(3,0,1,prime_list()).
p58(Side,Primes,Total,PL)->
	[A,B,C]=lists:map(fun(X)->Side*Side-(Side-1)*X end,[1,2,3]),
	PL ! {is_prime,A,self()},
	PL ! {is_prime,B,self()},
	PL ! {is_prime,C,self()},
	P=lists:sum(lists:map(fun(_)->receive {is_prime,_,true}->1;{is_prime,_,false}->0 end end,[a,a,a])),
	NPrimes=Primes+P,
	NTotal=Total+4,
	if
		NPrimes/NTotal < 0.1 -> io:format("~w~n",[Side]);
		true->p58(Side+2,NPrimes,NTotal,PL)
	end.

+-#PrimeList
class PrimeList
  @@primes=[2,3,5,7,11,13,17,19]

  def initialize
    @next=-1
  end

  def last
    return 0 if @next==-1
    PrimeList.get(@next)
  end

  def getNext
    PrimeList.get(@next+=1)
  end

  def [](i)
    PrimeList.get(i)
  end

  def PrimeList.isPrime?(n)
    if(@@primes[-1] >= n)
      return true if @@primes.index n
      return false
    end
    p=PrimeList.new
    sq=Math.sqrt(n)
    while(p.last<=sq)
      return false if n % (p.getNext)==0
    end
    true
  end

  def PrimeList.get(i)
    PrimeList.gen while @@primes.length<=i
    @@primes[i]
  end

  def PrimeList.getPrimeNear(n)
    PrimeList.gen until n<@@primes[-1]
    @@primes[PrimeList.primeIndexNear(n)]
  end  

  private

  def PrimeList.primeIndexNear(n)
    return 0 if n<@@primes[0]
    return [-1] if n>@@primes[-1]
    PrimeList.getIndexNear(@@primes,n)
  end

  def PrimeList.getIndexNear(list,n)
    return 0 if list.length==1
    if(list.length==2)
      avg=(list[0]+list[1])/2.0
      return 1 if n>avg
      return 0
    end
    splitAfter=list.size/2
    return PrimeList.getIndexNear(list[0..splitAfter],n) if n<list[splitAfter]
    return splitAfter+1+PrimeList.getIndexNear(list[(splitAfter+1)..-1],n) if n>list[splitAfter+1]
    avg=(list[splitAfter]+list[splitAfter+1])/2
    return splitAfter+1 if n>avg
    splitAfter
  end

  def PrimeList.gen
    add=@@primes[-1]
    cands=Set.new(1..(5*add)){|i|2*i+add}
    theBegin=add+2
    theEnd=11*add
    highest=Math.sqrt(theEnd).to_i
    upTo=PrimeList.primeIndexNear(highest)
    upTo-=1 if @@primes[upTo]>highest
    @@primes[1..upTo].each do |mult|
      ((theBegin-theBegin%mult)..(theEnd-theEnd%mult + mult)).step(mult){|i|cands.delete i}
    end
    @@primes=@@primes+cands.to_a.sort
  end
end

def get_layer(n)
  b=n*n
  m=n-1
  [b-m,b-2*m,b-3*m]
end

def p58
  tot=5.0
  count=3.0
  i=3
  while(count/tot >= 0.1)
    i+=2
    tot+=4
    count+=get_layer(i).select{|j|PrimeList.isPrime? j}.length
  end
  puts i
end