A double Mersenne number is a number of the form
 |
where 
is a Mersenne number. The first few double Mersenne
numbers are 1, 7, 127, 32767, 2147483647, 9223372036854775807, ... (OEIS A077585).
A double Mersenne number that is prime is called a double Mersenne prime. Since a Mersenne prime 
can be prime only for prime 
, a double Mersenne prime can be prime only for prime 
, i.e., 
a Mersenne prime. Double
Mersenne numbers are prime for 
, 3, 5, 7, corresponding to the sequence 7, 127, 2147483647,
170141183460469231731687303715884105727, ... (OEIS A077586).
The next four 
,
,
,
and 
have known factors summarized in the following table. The status of all other double
Mersenne numbers is unknown, with 
being the smallest unresolved case. Since this number
has 694127911065419642 digits, it is much too large for the usual Lucas-Lehmer
test to be practical. The only currently practical method of determining the
status of this number is therefore attempting to find small divisors (or discovery
of an efficient primality test for this type of
number).
Forbes (2004) organized an early distributed search for factors of 
. As of 2026, the DoubleMersennes.org distributed
search had found no factor of 
and had checked possible factors of the form 
through 
. Edgington maintains a list of known factorizations
of double Mersenne numbers.
 | factors/cofactor | reference |
| 13 | 338193759479 | Wilfrid Keller (1976) |
| 210206826754181103207028761697008013415622289 | Phil Moore (2003) | |
| C2410 | ||
| 17 | 231733529 | Raphael Robinson (1957) |
| 64296354767 | Wilfrid Keller (1981) | |
| C39438 | ||
| 19 | 62914441 | Raphael Robinson (1957) |
| 5746991873407 | Edgington and Keller (1994) | |
| 824271579602877114508714150039 | Phil Moore (2000) | |
| 2106734551102073202633922471 | Phil Moore (2003) | |
| 65997004087015989956123720407169 | Phil Moore (2011) | |
| 4565880376922810768406683467841114102689 | Phil Moore (2023) | |
| C157677 | ||
| 31 | 295257526626031 | Guy Haworth (1983, 1987) |
| 87054709261955177 | Keller (1994) | |
| 242557615644693265201 | Keiser and Forbes (1999) | |
| 178021379228511215367151 | Mayer (2005) | |
| C646456918 |
Where 
Is a Mersenne Prime." 
. Progress: 2 March 2004." 
."