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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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Some Thoughts similar series Comment 3 of 3 |

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
     prime
1       2       2
2       3       5
4       7       17
6       13      41
12      37      197
14      43      281
60      281     7699
64      311     8893
96      503     22039
100     541     24133
102     557     25237
108     593     28697
114     619     32353
122     673     37561
124     683     38921
130     733     43201
132     743     44683
146     839     55837
152     881     61027
158     929     66463
162     953     70241
178     1061    86453
192     1163    102001
198     1213    109147
204     1249    116533
206     1277    119069
208     1283    121631
214     1307    129419
216     1321    132059
296     1949    263171
308     2029    287137
326     2161    325019
328     2203    329401
330     2213    333821
332     2237    338279
334     2243    342761
342     2297    360979
350     2357    379667
356     2393    393961
358     2411    398771
426     2957    581921
446     3137    642869
458     3251    681257
460     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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