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%I #20 Dec 12 2019 05:34:57
%S 5,233,8783,24763,5828099,9229931,262707241,7717488553,34529828929,
%T 311995561321,549120448879,33777547344991
%N Smallest prime p such that the sum of cubes of all primes up to p is a multiple of 10^n.
%C Suggested in a discussion in Mersenneforum, with contributions by users "davar55", _Charles R Greathouse IV_, and _Benjamin R. Buhrow_. The latter calculated terms a(1)-a(12) of this sequence (see links).
%H Ben Buhrow, <a href="http://sites.google.com/site/bbuhrow/home/sums-of-prime-squares">Software and extended tables</a>, 07 Apr 2010.
%H Ben Buhrow and others, <a href="https://www.mersenneforum.org/showthread.php?t=13181&page=4">Sums of Squares</a>, thread in Mersenneforum, April 2010.
%e a(1): 10 divides prime cube sum up to 5, sum = 2^3 + 3^3 + 5^3 = 160;
%e a(2): 100 divides prime cube sum up to 233, sum = 143309500;
%e a(3): 1000 divides prime cube sum up to 8783, sum = 167992435025000.
%o (PARI) for(n=1,8,my(n10=10^n,s=0);forprime(p=2,oo,s+=p^3;if(!(s%n10),print1(p,", ");break)))
%Y Cf. A174106, A174862, A330309.
%K nonn,more,hard
%O 1,1
%A _Hugo Pfoertner_, Dec 10 2019
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