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Build a triangle from all positive integers in the following way:

1 
 2  3 
 4  5  6 
 7  8  9 10 11 12 13 14 15 
16 17 18 19 20 21 
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 
46 47 48 49 50 51 52 53 54 55 
56 57 58 59 60 61 62 63 64 65 66 
. . .

Each positive integer has up to eight neighbours in the triangle.

A set of three primes is called a prime triplet if one of the three primes has the other two as neighbours in the triangle.

For example, in the second row, the prime numbers 2 and 3 are elements of some prime triplet.

If row 8 is considered, it contains two primes which are elements of some prime triplet, i.e. 29 and 31. 
If row 9 is considered, it contains only one prime which is an element of some prime triplet: 37.

Define S(<var>n</var>) as the sum of the primes in row <var>n</var> which are elements of any prime triplet. 
Then S(8)=60 and S(9)=37.

You are given that S(10000)=950007619.

Find  S(5678027) + S(7208785).

​x
 
<p>Build a triangle from all positive integers in the following way:</p>​<p style="font-family:'courier new', monospace;font-weight:bold;margin-left:50px;"> 1<br /> <span style="color:#FF0000;">2</span>  <span style="color:#FF0000;">3</span><br /> 4  <span style="color:#FF0000;">5</span>  6<br /> <span style="color:#FF0000;">7</span>  8  9 10<br /><span style="color:#FF0000;">11</span> 12 <span style="color:#FF0000;">13</span> 14 15<br />16 <span style="color:#FF0000;">17</span> 18 <span style="color:#FF0000;">19</span> 20 21<br />22 <span style="color:#FF0000;">23</span> 24 25 26 27 28<br /><span style="color:#FF0000;">29</span> 30 <span style="color:#FF0000;">31</span> 32 33 34 35 36<br /><span style="color:#FF0000;">37</span> 38 39 40 <span style="color:#FF0000;">41</span> 42 <span style="color:#FF0000;">43</span> 44 45<br />46 <span style="color:#FF0000;">47</span> 48 49 50 51 52 <span style="color:#FF0000;">53</span> 54 55<br />56 57 58 <span style="color:#FF0000;">59</span> 60 <span style="color:#FF0000;">61</span> 62 63 64 65 66<br />. . .</p>​<p>Each positive integer has up to eight neighbours in the triangle.</p>​<p>A set of three primes is called a <i>prime triplet</i> if one of the three primes has the other two as neighbours in the triangle.</p>​<p>For example, in the second row, the prime numbers 2 and 3 are elements of some prime triplet.</p>​<p>If row 8 is considered, it contains two primes which are elements of some prime triplet, i.e. 29 and 31.<br />If row 9 is considered, it contains only one prime which is an element of some prime triplet: 37.</p>​<p>Define S(<var>n</var>) as the sum of the primes in row <var>n</var> which are elements of any prime triplet.<br />Then S(8)=60 and S(9)=37.</p>​<p>You are given that S(10000)=950007619.</p>​<p>Find  S(5678027) + S(7208785).</p>

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