[davar55]

Originally Posted by davar55

Another possibly interesting variation:

2^2 + 3^3 + 5^5 + ... + p^p = 10^mK

What is the smallest prime p such that
the sum of squares of all primes up to p
is a multiple of 10 (or 100 or 1000 and so on).

(I think somewhere in these series we'll get
numeric pointers to empirical evidence
connecting some number theoretical conjectures.)

Just checking.