View Single Post
Old 2018-12-11, 08:28   #1
Mar 2018

17×31 Posts
Default 541456 and 51456. I checked 20 numbers 2000 times and found 200 patterns!!

pg(k)=M(k)||M(k-1) where || denotes concatenation base 10 and M(k) is the k-th 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 (541456-51456=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?
enzocreti is offline   Reply With Quote