Quote:
Originally Posted by Fan Ming
I agree with that. Most likely MM127 is not prime, thus primes in CatalanMersenne sequence end at M127.

I think it is not prime because it is corresponding to the number 5
Like the case of
Fermat numbers:
F0=3 is prime, F1=5 is prime, F2=17 is prime, F3=257 is prime, F4=65537 is prime, but F5=4294967297=641*6700417 is composite, and Fn is composite at least for 5<=n<=32
In the case of
CatalanMersenne numbers:
C0=2 is prime, C1=3 is prime, C2=7 is prime, C3=127 is prime, C4=170141183460469231731687303715884105727 is prime, but I think that C5 is composite, of course if C5 is composite, then Cn is composite for all n>=5
Fn = (F(n1)1)^2+1, F0 = 3
Cn = 2^C(n1)1, C0 = 2
There is another sequence highly related to these numbers,
Double Mersenne numbers:
Define Dn = MM(nth prime)
D1=7 is prime, D2=127 is prime, D3=2147483647 is prime, D4=170141183460469231731687303715884105727 is prime, but Dn is composite at least for 5<=n<=17
I think that Fn, Cn, and Dn are primes only for n<=4, and composite for n>4
(think about that: polynomial equations with degree n have algebraic solution if and only if n<=4)