A330308 Smallest prime p such that the sum of cubes of all primes up to p is a multiple of 10^n.

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

Offset: 1

Author

Hugo Pfoertner, Dec 10 2019

Keywords

• nonn
• more
• hard

Comments

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).

Examples

			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.
		

Links

• Ben Buhrow, Software and extended tables, 07 Apr 2010.
• Ben Buhrow and others, Sums of Squares, thread in Mersenneforum, April 2010.

Crossrefs

Cf. A174106, A174862, A330309.

Programs

PARI

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