statement.html

problem 58 · 11 lines

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<p>Starting with $1$ and spiralling anticlockwise in the following way, a square spiral with side length $7$ is formed.</p>
<p class="center monospace"><span class="red"><b>37</b></span> 36 35 34 33 32 <span class="red"><b>31</b></span><br/>
38 <span class="red"><b>17</b></span> 16 15 14 <span class="red"><b>13</b></span> 30<br/>
39 18 <span class="red"> <b>5</b></span>  4 <span class="red"> <b>3</b></span> 12 29<br/>
40 19  6  1  2 11 28<br/>
41 20 <span class="red"> <b>7</b></span>  8  9 10 27<br/>
42 21 22 23 24 25 26<br/><span class="red"><b>43</b></span> 44 45 46 47 48 49</p>
<p>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 $8/13 \approx 62\%$.</p>
<p>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 $10\%$?</p>
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