Sums of Primes

Site for tabulation of sums of primes, prime squares, prime cubes and various interesting properties of them.

This site is a work in progress.

Prompted by the mersenneforum puzzle, I created a routine within YAFU (to leverage its prime generation capabilities) to sum squares of primes and test them for multiplicity of power of 10. Charles R. Greathouse found the first several terms using a PARI one-liner. These were verified by my routine and extended to include sums of primes up to 30 trillion, as of 31 March 2010.

This sequence appears in the OEIS, reference A174862.

I've also looked at sums of primes. This sequence will be submitted to OEIS soon.

And sums of primes cubes. Searched up to 10 trillion as of 7 April 2010

The attached spreadsheet contains the prime, prime square, and prime cube sums in increments of 1 billion integers. These can be fed into my program for sequence continuation, which someday I may return to.

On a X5570 Xeon CPU, finding primes in each range of 1e9 takes about 3 seconds, and summing the primes/squares/cubes in that range (~ 30 - 40 million primes, depending on the interval) takes a fraction of a second (0.1 - 0.3 seconds).