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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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Those k that are even all include the first prime, 2, and so have only one example: the first k primes. Extending beyond a sum of 300 are:

`k     last     sum      prime1       2       22       3       54       7       176       13      4112      37      19714      43      28160      281     769964      311     889396      503     22039100     541     24133102     557     25237108     593     28697114     619     32353122     673     37561124     683     38921130     733     43201132     743     44683146     839     55837152     881     61027158     929     66463162     953     70241178     1061    86453192     1163    102001198     1213    109147204     1249    116533206     1277    119069208     1283    121631214     1307    129419216     1321    132059296     1949    263171308     2029    287137326     2161    325019328     2203    329401330     2213    333821332     2237    338279334     2243    342761342     2297    360979350     2357    379667356     2393    393961358     2411    398771426     2957    581921446     3137    642869458     3251    681257460     3257    687767`

These are the topic fo Sloane's A013917 and A013916

 Posted by Charlie on 2012-03-27 22:38:03

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