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