

A330308


Smallest prime p such that the sum of cubes of all primes up to p is a multiple of 10^n.


2



5, 233, 8783, 24763, 5828099, 9229931, 262707241, 7717488553, 34529828929, 311995561321, 549120448879, 33777547344991
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OFFSET

1,1


COMMENTS



LINKS

Ben Buhrow and others, Sums of Squares, thread in Mersenneforum, April 2010.


EXAMPLE

a(1): 10 divides prime cube sum up to 5, sum = 2^3 + 3^3 + 5^3 = 160;
a(2): 100 divides prime cube sum up to 233, sum = 143309500;
a(3): 1000 divides prime cube sum up to 8783, sum = 167992435025000.


PROG

(PARI) for(n=1, 8, my(n10=10^n, s=0); forprime(p=2, oo, s+=p^3; if(!(s%n10), print1(p, ", "); break)))


CROSSREFS



KEYWORD

nonn,more,hard


AUTHOR



STATUS

approved



