An Euler number prime is an Euler number E_n such that the absolute value left bracketing bar E_n right bracketing bar is prime (the absolute value is needed since E_n takes on alternating positive and negative values for even indices). Note that these numbers are distinct from a different type of prime known as Euler primes. The first few Euler number primes E_n occur for n = 4, 6, 38, 454, 510, ... (OEIS A103234), corresponding to 5, -61, -23489580527043108252017828576198947741, ... (OEIS A092823). As of February 2022, the largest known prime Euler number is left bracketing bar E_510 right bracketing bar , which has 1062 decimal digits and was proven to be prime by D. Broadhurst in 2002.

Euler number | Euler prime | integer sequence primes | prime number