This number is a probable-prime (likely to be a prime but we have not (re-)proven it on this site).
Just showing those entries submitted by 'Carmody': (Click here to show all)
The first 2780 digits of the decimal expansion of e is a (probable, SPRP and SLPRP) prime. (As of mid-2004, no larger examples are known within the leading digits of e, tested to 20000 digits.) [Carmody]