A double Mersenne number is a number of the form
 |
where 
is a positive integer and 
is a Mersenne number.
The first few double Mersenne numbers are 1, 7, 127, 32767, 2147483647, 9223372036854775807,
... (OEIS A077585, omitting its initial term
0).
A double Mersenne number that is prime is called a double Mersenne prime. Since a Mersenne number 
can be prime
only for prime 
, a double Mersenne prime requires 
to be a Mersenne prime,
which in turn requires 
to be 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. Among the remaining cases for
which 
is a Mersenne prime, the smallest unresolved case
is 
.
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." 
." 