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Prime = Sqrt of Summed Primes (Posted on 2011-03-06) Difficulty: 3 of 5

No Solution Yet Submitted by brianjn    
Rating: 2.0000 (1 votes)

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Solution computer solution (spoiler) | Comment 1 of 6

   10   FirstPrime=2
   20   while FirstPrime<500
   30      for N=2 to 9
   40        T=0
   50        P=FirstPrime
   60        for I=1 to N
   70          T=T+P
   80          LastPrime=P
   90          P=nxtprm(P)
  100        next I
  110        Sr=int(sqrt(T)+0.5)
  120        if Sr*Sr=T and prmdiv(Sr)=Sr then print FirstPrime;LastPrime;N,T;Sr
  130      next N
  140      FirstPrime=nxtprm(FirstPrime)
  150   wend

doesn't check to see that the subsequent primes fall under 500 but in fact all do, as shown in the printout that, among other things shows the last prime in each sequence:

first  last    N   sum square
prime  prime            root
  13     19    3    49    7 
  13     37    7   169   13
  37     43    3   121   11
  73    109    9   841   29
 181    199    5   961   31
 227    269    9  2209   47
 277    283    3   841   29
 293    337    7  2209   47
 313    331    3   961   31
 317    349    5  1681   41


 
To see all the primes involved rather than just the first and last, below, all the summed primes are listed on a line below each main report line:

 13  19  3       49  7
 13  17  19
 13  37  7       169  13
 13  17  19  23  29  31  37
 37  43  3       121  11
 37  41  43
 73  109  9      841  29
 73  79  83  89  97  101  103  107  109
 181  199  5     961  31
 181  191  193  197  199
 227  269  9     2209  47
 227  229  233  239  241  251  257  263  269
 277  283  3     841  29
 277  281  283
 293  337  7     2209  47
 293  307  311  313  317  331  337
 313  331  3     961  31
 313  317  331
 317  349  5     1681  41
 317  331  337  347  349

  Posted by Charlie on 2011-03-06 18:09:43
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