brainwagon

Over at Neighborhood of Infinity, there’s a mention that the Angels and Devil game might have been solved. Don’t know what it is? It’s a game played on an infinite checkboard. The Angel begins at the origin, and can move to any square that can be reached in k moves of a chess king. The [...]

If you take the sequence of primes, and concatenate the first n of them together, how many of these are prime? It’s not hard to see that 2, 23, and even 2357 is prime. The next term has 355 digits: 235711131719232931374143475359616771737983899710110\ 310710911312713113713914915115716316717317918119119\ 319719921122322722923323924125125726326927127728128\ 329330731131331733133734734935335936737337938338939\ 740140941942143143343944344945746146346747948749149\ 950350952152354154755756356957157758759359960160761\ 3617619631641643647653659661673677683691701709719 The concatenation of primes up until 1033 also [...]