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    $\begingroup$ you are way too humble! calculating your sum for even the first 2000 primes takes less than a second. However, is there a way to get around storing large numbers in sums in memory? It keeps crashing my computer when I try toPrime=5000. $\endgroup$ Commented Mar 26, 2013 at 6:03
  • $\begingroup$ +1 (that's freaking fast!) Can you explain why Accumulate@FoldList[#1 #2 &, 1, Range[n] is so much quicker to Accumulate@Array[#! &, n] + 1? I really don't get it. $\endgroup$ Commented Mar 26, 2013 at 11:23
  • $\begingroup$ @gpap Calculating factorial so many times costs a lot. Since we know we want all the factorials up to Prime[toPrime]-1, we ultimately gain a lot keeping the intermediate results with FoldList. $\endgroup$ Commented Mar 26, 2013 at 12:04
  • $\begingroup$ @MichaelE2 Yes, worked it out myself in the meantime - you multiply the previous result and don't calculate a factorial at every step. Thanks $\endgroup$ Commented Mar 26, 2013 at 12:11
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    $\begingroup$ Is there any reason why you used #1 #2 & instead of Times? $\endgroup$ Commented Jun 15, 2015 at 12:53