An 
-prime is a prime number appearing in
the decimal expansion of e. The first few are 2, 271,
2718281, 2718281828459045235360287471352662497757247093699959574966967627724076630353547594571,
... (OEIS A007512). The numbers of digits in
these examples are 1, 3, 7, 85, 1781, 2780, 112280, 155025, ... (OEIS A064118).
The following table summarizes the largest known such primes.
 | discoverer |
| 2780 | E. W. Weisstein
(Jan. 17, 2005) |
| 112280 | E. W. Weisstein
(Jul. 3, 2009) |
| 155025 | E. W. Weisstein
(Oct. 11, 2010) |
Another set of 
-related
primes is the positive integers 
such that 
is prime, where 
is the floor function.
The first few are 1, 2, 18, 50, 127, 141, 267, 310, 2290, 4487, 5391, ... (OEIS A050808), corresponding to the primes 2, 7, 65659969,
5184705528587072464087, ... (OEIS A050809).
Similarly, the first few 
such that ![[e^n]](https://speed.lescigales.org/xypor/index.php?q=aHR0cHM6Ly9tYXRod29ybGQud29sZnJhbS5jb20vaW1hZ2VzL2VxdWF0aW9ucy9lLVByaW1lL0lubGluZTguc3Zn)
is prime, where ![[x]](https://speed.lescigales.org/xypor/index.php?q=aHR0cHM6Ly9tYXRod29ybGQud29sZnJhbS5jb20vaW1hZ2VzL2VxdWF0aW9ucy9lLVByaW1lL0lubGluZTkuc3Zn)
is the ceiling function are 1, 5, 7, 10, 105,
... (OEIS A059303), with no others less than
, corresponding to the primes 3, 149,
1097, 22027, 3989519570547215850763757278730095398677254309, ... (OEIS A118840).
The first 
-digit
primes (excluding numbers with leading zeros) in the decimal expansion of 
for 
,
2, ... are 2, 71, 271, 4523, 74713, 904523, 2718281, 72407663, ... (OEIS A095935),
which occur at positions 0, 1, 0, 14, 24, 12, 0, 64, 19, 99, 37, 53, ... (OEIS A115019), counting the leading 2 in the decimal
expansion of 
as position 0.