Mark wrote:

> Puzzle: What is special about these 10 consecutive primes?

>

> 5981567

> 5981579

> 5981609

> ...

> 5981683

Solved within a minute by searching the first term in OEIS:

http://oeis.org/A214219
That may seem like cheating but this property looks difficult to guess.

So for each k from 1 to 10, k divides the sum of the

k consecutive primes starting at 5981567:

1 divides 5981567

2 divides 5981567 + 5981579

3 divides 5981567 + 5981579 + 5981609

...

10 divides 5981567 + ... + 5981683.

A214219 and

http://www.primepuzzles.net/puzzles/puzz_415.htm
also give two more terms:

148871869 for k = 1 to 11, and 5545986967 for k = 1 to 12.

My computation agrees and shows 28511128379 for k = 1 to 13,

and 85185688439 for k = 1 to 14.

--

Jens Kruse Andersen