May 2004
New York City
2^{3}×23^{2} Posts

From this thread:
Quote:
Originally Posted by davar55
2^2 + 3^2 + 5^2 + ... + p^2 = 10^{m}K
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).

Quote:
Originally Posted by CRGreathouse
907, 977, 977, 36643, 1067749, 17777197, 71622461, 2389799983, ...
The next term (if one exists) is more than 4 trillion.

Quote:
Originally Posted by cheesehead
Not yet in the OEIS.
http://www.research.att.com/~njas/sequences/
I think it qualifies. Also, I'm fond of OEIS entries with relatively large initial terms  especially when the next few terms are so closely spaced as in this one. (Might it set some record in that regard  highest ratio of initial term to average spacing of next n terms, for n = 3?)
I'd be glad to submit it, but I think it should be one of you guys.
How about generalizing to other bases?

Quote:
Originally Posted by davar55
This is fine work by all of you. If you wish to submit the sequence to
oeis, please go ahead. I couldn't do justice to the calculations, which
I'm really impressed by. Joint discovery (attribution) is fine.

Quote:
Originally Posted by bsquared

Quote:
Originally Posted by davar55
With all the work done on the OP, it shouldn't be too hard
to generalize the problem a bit.
I think cubes.
2^3 + 3^3 + 5^3 + ... + p^3 = 10^{m}K
What is the smallest prime p such that
the sum of cubes of all primes up to p
is a multiple of 10 (or 100 or 1000 or 10000 or ...).
I'm also curious about how these (squares and cubes) results
compare to first powers (sum of primes themselves).
Since these series depend on the properties of a number
in base ten, they could be considered recreational 
interesting but not necessarily useful. Still, perhaps the
sequence of sequences can someday be used to derive some
important number theoretic fact. That's one of the purposes
of the oeis.

Yes indeed.
