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Old 2021-09-15, 03:37   #11
slandrum
 
Jan 2021
California

22·3·19 Posts
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Quote:
Originally Posted by T.Rex View Post
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 1-4..... 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.

Last fiddled with by slandrum on 2021-09-15 at 03:40
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