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  • $\begingroup$ @S. Carnahan:i am not convinced , how many numbers until this are out of the cover? compare it with the 2^k (where k is this number). i think that the question remains full open $\endgroup$ Commented Nov 18, 2011 at 16:42
  • $\begingroup$ There are 40 integers which will for sure never get covered . The largest is 99. The largest prime used is under 100,000 and the smallest uncovered integer (after 99) is well over 110,000. The calculations carry on a bit further than shown. $\endgroup$ Commented Nov 18, 2011 at 17:05
  • $\begingroup$ Aaron,your method of the semi-greedy strategy (greedy from a number and over ) is interesting and i want to thank you very much for your efforts and your interest ,but the question whether the non-sieved numbers from these greedy methods grow faster than the primes is ,as it seems, too sharp to be answered analytically(?). 2^40 >> 110,000 so... $\endgroup$ Commented Nov 18, 2011 at 17:16
  • $\begingroup$ If I have time maybe I will try to tune it up a bit. I might be able to get the missed numbers to be a smaller set if I did not care that some were relatively large. Gerhard would seem to prefer that we miss 59 integers less than 90 (if possible) $\endgroup$ Commented Nov 18, 2011 at 18:54
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    $\begingroup$ ImageShack seems to have deleted your image and replaced it with an ad banner. If you still have it (or can reproduce it), please reupload to the SE imgur account using the image upload button in the editor toolbar. $\endgroup$ Commented Aug 29, 2015 at 21:24