First we start with a list of prime numbers, then write the cumulative sums for the prime numbers (these images were taken with my laptop camera off a whiteboard): My method for computing P(n,k) is pretty simple. ![]() How big is P(2011,k) compared to, the number of primes less than or equal 2011? Let us write P(n,k) as the number of primes less than or equal to n that can be written as a sum of at least k consecutive primes. Naturally I wonder, how rare are these numbers - numbers that are prime but also a sum of a bunch of consecutive primes? This seems like a problem easily solved with some programming. ![]() Furthermore (as I already said), 2011 is prime. Not only that, but according to numerous math bloggers and twitterers on the internet, 2011 is the sum of 11 consecutive primes - that is, 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211.
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