Prime Sum

Let

$$\Sigma(n)\equiv \sum_{i=1}^n p_i$$

be the sum of the first $n$ Primes. The first few terms are 2, 5, 10, 17, 28, 41, 58, 77, ... (Sloane's A007504). Bach and Shallit (1996) show that

$$\Sigma(n)\sim {n^2\over 2\log n},$$

and provide a general technique for estimating such sums.

See also Primorial

References

Bach, E. and Shallit, J. §2.7 in Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, 1996.

Sloane, N. J. A. Sequence A007504/M1370 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.