Find the largest number that cannot be written
as a sum of distinct primes of the form 6*n+1.
Well as it's entitled 'mission impossible' I assume there is no such largest number.
But is it true?
Consider this range:
1 331 331
2 332 109+223
3 333 13+43+277
4 334 13+31+109+181
5 335 13+19+31+61+211
6 336 13+19+31+37+79+157
7 337 337
8 338 7+331
9 339 7+332
10 340 7+333
11 341 7+334
12 342 7+335
13 343 7+336
14 344 7+337
15 345 13+332
16 346 (19+7)+43+277
17 347 (19+7)+31+109+181
18 348 13+19+31+37+97+151
19 349 349
20 350 19+331 etc.
We could have selected a higher starting number and left out both 7 and 13 to start with, or 7 and 13 and 19, etc. and still obtain a series of indefinite length that could be extended by adding 7,13,19,etc. to earlier solutions in the series that did not themselves contain those small primes.
Edited on August 27, 2013, 5:30 am

Posted by broll
on 20130827 05:28:06 