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Old 2018-12-11, 08:28   #1
enzocreti
 
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?
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