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Old 2011-01-23, 03:52   #179
davar55
 
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May 2004
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Quote:
Originally Posted by davar55 View Post
Another possibly interesting variation:

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

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.
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