How many primes between 6!+2 and 6!+6. Is there an quick way to do this without multiply out 6!? Just wondering incase we get something much larger like 20!.
Hi gmatusa2010 ... Interesting Q ... Thanks !
6! + 3 = 3 times (1.2.4.5.6 + 1) = 3 times <some integer>; Hence, not a prime
6! + 4 = 4 times (1.2.3.5.6 + 1) = 4 times <some integer>; Hence, not a prime
6! + 5 = 5 times (1.2.3.4.6 + 1) = 5 times <some integer>; Hence, not a prime
To make it more interesting, what would be the first number after 6! which is a prime number?
Would it be 6! + 7 ? Because 6! is not a multiple of 7? But, this only says that 6! + 7 is not a multiple of 7 ... It could be a multiple of some other integer ... 727 is indeed a prime # ... But, I do not suppose it can be generalized ... This is just a coincidence ...
In other words, is there a method to find the least value of b such that "a! + b" is a prime number ???
