I checked the prime factors of
$$\sum_{k=1}^{30}k^{k^k}$$
and did not find any upto $10^8$
Are there any useful restrictions to accelerate the search ?
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$\begingroup$ This is an interesting question on it's own, but could you tell us how did this come up? $\endgroup$– chubakuenoCommented Feb 11, 2014 at 0:30
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$\begingroup$ I just searched the smallest prime factors of z(n) := $\sum_{k=1}^nk^{k^k}$ and the largest one occured for n=9 (it is 205991). And n=30 is the least n, such that z(n) has no small prime factors. $\endgroup$– PeterCommented Feb 11, 2014 at 0:32
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$\begingroup$ How are you currently doing this? $\endgroup$– chubakuenoCommented Feb 11, 2014 at 0:58
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$\begingroup$ I use the powermod routine to calculate z(n) mod p $\endgroup$– PeterCommented Feb 11, 2014 at 1:00
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$\begingroup$ I have several ideas on how to test primes faster(FLT, sieving), but no one on how to dismiss primes without testing them, and I don't want to be redundant. Please show your current method to see if I can do any improvement to it(or if your method is better than the one I have in mind I would like to see it) $\endgroup$– chubakuenoCommented Feb 11, 2014 at 1:09
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