Euler Number Prime
المؤلف:
Sloane, N. J. A.
المصدر:
Sequences A092823 and A103234 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
22-9-2020
1168
Euler Number Prime
An Euler number prime is an Euler number 
such that the absolute value 
is prime (the absolute value is needed since 
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 
occur for 
, 6, 38, 454, 510, ... (OEIS A103234), corresponding to 5, 
, 
, ... (OEIS A092823).
As of August 2020, the largest known prime Euler number is 
, which has 1062 decimal digits and was proven to be prime by D. Broadhurst in 2002.
The following table summarizes searches for larger Euler number primes, of which there are none up to a limit of at least 
.
| search limit |
date |
searcher |
| 28688 |
Mar. 21, 2009 |
E. Weisstein |
| 69574 |
Aug. 21, 2020 |
S. Plouffe |
REFERENCES:
Sloane, N. J. A. Sequences A092823 and A103234 in "The On-Line Encyclopedia of Integer Sequences."
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