541456 and 51456. I checked 20 numbers 2000 times and found 200 patterns!!
pg(k)=M(k)M(k1) where  denotes concatenation base 10 and M(k) is the kth Mersenne number. Examples of such numbers are 1023511, 255127, 12763...
I found that pg(k) is prime for k=51456 and for k=541456.
I wonder if that is only a coincidence (54145651456=700^2) or there is an hidden structure undermeath these numbers. What is the probability to have by mere chance two probable primes with these two amazing exponents?
