A triple check may be one of two things:
- A third Lucas-Lehmer test performed on an exponent when the residues from the intial test and the double check don't match. If the residues match, then the number is known to be composite, (this assumes that the residue is not zero, otherwise it is prime).
- A second independant verification that a number is in fact prime. Any claim that a number is a new Mersenne prime must be verified (double checked) on a computer of a different hardware architecture (family of processor) and using different software. If a new Mersenne prime is found using Prime95 on a computer using a CPU of the Pentium family, then to protect against some error in either software or hardware design or manufacture, the number will be tested using Mlucas or Glucas on a computer using an Itanium, Alpha, or other type of CPU. Generally both will occur, thus one becoming a "triple check". In the future Mlucas.cuda run on a GPU will form a very good independant triple check.