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Some sums (Posted on 2012-03-26) Difficulty: 3 of 5
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    
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Solution 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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