This number is a prime.
7841 is the smallest prime p such that (p!-1) is divisible by nextprime to p. Stuart Gascoigne discovered this and two more solutions. No other solutions known (June 2019). [Rivera]
The first case of a prime such that removing respectively the last and first digit one obtains two consecutive perfect squares: 28²=784 and 29²=841. Moreover, notice that 28 and 29 are the possible number of days in the month of February, and 28 is a perfect number while 29 is another prime. [Leonardis]