mersenneforum.org - View Single Post - 541456 and 51456. I checked 20 numbers 2000 times and found 200 patterns!!

enzocreti · 2018-12-11, 08:28

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?

2018-12-11, 08:28	#1
enzocreti Mar 2018 17×31 Posts	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?