Quote:
Originally Posted by T.Rex
I found this papier very interesting:
https://faculty.math.illinois.edu/~j...nneBenford.pdfhttps://faculty.math.illinois.edu/~j...nneBenford.pdf
First, it seems to say that Mersenne primes are random.
Second, it means that looking at Mersenne exponents starting with 1,2,3, or 4 generates 3 times more primes than exponents starting with 5,6,7,8, or 9. Thus, should the GIMPS look first at these 14..... exponents?
Code:
1 13
2 10
3 7
4 5
5 2
6 3
7 2
8 3
9 2

That's due to logarithmic bias. You take any sequence that increases exponentially (which the mersenne exponents do approximately) and you'll see a similar pattern in the leading digit. It actually gives no indication about where you can find the next mersenne prime, other than they get scarcer as the exponents get larger.