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 Prime = Sqrt of Summed Primes (Posted on 2011-03-06)

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

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 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 squareprime  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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