A330308 - OEIS

%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&amp;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