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 Some sums (Posted on 2012-03-26)
The sum of k consecutive primes is a prime number.
List all the possibilties for k=2,3,5 and 7 with the sums under 300.

 See The Solution Submitted by Ady TZIDON No Rating

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 computer solution--extended to all values of k | Comment 2 of 3 |

Even values of k must of course start with 2, and so are the sum of the first k primes, as there needs to be an odd number of odd primes. k = 4, 6, 12 and 14 in fact work. Above k=14, there is no solution with the sum being under 300.

` k      first and        last primes      sum 2 2       2  3            5  3 3       5  11           23 3       7  13           31 3       11  17          41 3       17  23          59 3       19  29          71 3       23  31          83 3       29  37          97 3       31  41          109 3       41  47          131 3       53  61          173 3       61  71          199 3       67  73          211 3       71  79          223 3       79  89          251 3       83  97          269 4 4       2  7            17 5 5       5  17           53 5       7  19           67 5       11  23          83 5       13  29          101 5       19  37          139 5       29  43          181 5       31  47          199 5       43  61          263 6 6       2  13           41 7 7       17  41          197 7       19  43          223 7       23  47          251 7       29  53          281 8 9 9       3  29           127  10 11 11      5  41           233 11      7  43           271 12 12      2  37           197 13 14 14      2  43           281`

5   dim H(21)
10    for K=2 to 14
15   print K
20      P=0:Tot=0:Ct=0:erase H():dim H(21)
30      while P<2000
40        P=nxtprm(P)
50        Tot=Tot-H(1)
60        for I=1 to K-1
70          H(I)=H(I+1)
80        next I
90        H(K)=P
100        Tot=Tot+P:inc Ct
110        if prmdiv(Tot)=Tot and Tot<300 and Ct>=K then print K,H(1);H(K),Tot
120      wend
130    next K

 Posted by Charlie on 2012-03-26 11:35:23

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