# Are all prime numbers Mersenne prime? [closed]

Sorry if this is a duplicate of a post, but I having trouble finding the answer anywhere. Are all prime numbers Mersenne prime? Or are there any numbers in between Mersenne primes?

• $5$ isn't...... Aug 2 at 14:34
• $2$ isn't........ Aug 2 at 14:34
• I suppose lots of them aren't. Did you do an internet search? en.wikipedia.org/wiki/Mersenne_prime Aug 2 at 14:35
• Of course not, but the largest known are Mersenne and the most other of the largest generalized Fermat primes since they are easiest to be proven prime and moreover give a better chance to find a prime than if one would take a random number. Aug 2 at 14:36
• Sorry, I assumed 2, 3, and 5 were prime and started calculating from these.
– Matt
Aug 2 at 14:38

All Mersenne primes are prime numbers, but the converse is not necessarily true. A Mersenne prime is $$2^k - 1$$, where $$k$$ is a positive integer greater than or equal to 2. Examples of Mersenne primes are $$3$$, $$7$$, and $$31$$. These are all also regular primes. However, counterexamples of primes that are NOT Mersenne primes are (as shown in the comments), $$2$$, $$5$$, or $$11.$$