2 ms·

Concrete examples: 3!+1 = 7 is prime 11!+1 = 39916801 is prime (according to http://www.wolframalpha.com/input/?i=is+11!%2B1+prime%3F http://www.wolframalpha.

• btilly 13y ago
  You forgot a couple. 1!+1 = 2 is prime. 2!+1 = 3 is prime. Based on a back of the envelope estimate, the number of values of n up to N for which n!+1 is prime should be O(log(log(N))) so it should happen infinitely often. But proving that is likely to be difficult.
  • xyzzyz 13y ago
    Did you get that estimate by some other way than using prime number theorem and Stirling approximation for n! ?
    • btilly 13y ago
      That is exactly how I estimated it. But when I think about it, it is the wrong way to estimate it. Because you've eliminated all of the most common causes of those numbers not being prime, so the density of primes in that set should be expected to be massively higher than normal. If I thought about it, I could come up with a much better estimate. But it would take some thought.