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Forum: Dobri 2021-07-17, 20:41
Replies: 49
Views: 3,012
Posted By Dobri
Strategies for Manual Testing

Closing the thread at
https://mersenneforum.org/showthread.php?t=26997
was premature because the OP was not given a chance to respond, especially at a stage when a post was submitted in their...
Forum: Dobri 2021-07-17, 16:21
Replies: 49
Views: 3,012
Posted By Dobri
It is not a matter of convenience. Simply there...

It is not a matter of convenience. Simply there is no rush to spill the beans in a single post.
For instance, attached are the base-2 distributions.
In the second image, the base-10 distributions...
Forum: Dobri 2021-07-17, 12:24
Replies: 49
Views: 3,012
Posted By Dobri
The idea is not to predict the next Mp but rather...

The idea is not to predict the next Mp but rather select suitable options for manual testing.
Assuming that there are several Mp in the 9-digit range, one would expect that at least one is among the...
Forum: Dobri 2021-07-17, 12:13
Replies: 49
Views: 3,012
Posted By Dobri
Lightbulb Digit Sum Distributions of Mersenne-Number Exponents

The attached image contains the plots of:
- The digit sum distribution of known Mersenne-prime exponents (green dots) in the interval [2, 47];
- The digit sum distribution of 8-digit...
Forum: Dobri 2021-07-16, 17:36
Replies: 49
Views: 3,012
Posted By Dobri
Indeed, Mn=49,999,991 (digit sum 59) could have...

Indeed, Mn=49,999,991 (digit sum 59) could have been an Mp but it has been factored instead.
Forum: Dobri 2021-07-16, 16:50
Replies: 49
Views: 3,012
Posted By Dobri
Lightbulb Let's mention also another empirical observation...

Let's mention also another empirical observation which might be obvious but related to this thread nonetheless.

When comparing the digit sum histograms of the Mersenne-prime (Mp) and...
Forum: Dobri 2021-07-15, 12:29
Replies: 49
Views: 3,012
Posted By Dobri
I myself am undecided to what extent incomplete...

I myself am undecided to what extent incomplete patterns could produce tangible results in number theory.
The digit sum histogram is just one partial pattern characteristic among many alternative...
Forum: Dobri 2021-07-15, 11:48
Replies: 49
Views: 3,012
Posted By Dobri
Oscillations around the linear fit are common but...

Oscillations around the linear fit are common but to have a change in slope for a dozen consecutive Mersenne primes from M40 till M51 and assume that it is happening just by chance would be in blind...
Forum: Dobri 2021-07-14, 20:03
Replies: 49
Views: 3,012
Posted By Dobri
This is an early attempt to eventually improve...

This is an early attempt to eventually improve the competitiveness of Mersenneries with modest resources.
I am still figuring out to what extent the combination of digit sum histograms obtained for...
Forum: Dobri 2021-07-14, 19:08
Replies: 49
Views: 3,012
Posted By Dobri
The effort to fit the pre-GIMPS Mersenne primes...

The effort to fit the pre-GIMPS Mersenne primes with a line using e^(-gamma) from the Mertens' third theorem (which is valid for ALL primes) is based on the assumption that the Mersenne primes have...
Forum: Dobri 2021-07-14, 04:18
Replies: 49
Views: 3,012
Posted By Dobri
We keep doing DC for mostly 8-digit exponents...

We keep doing DC for mostly 8-digit exponents indeed. :)
Forum: Dobri 2021-07-14, 03:37
Replies: 49
Views: 3,012
Posted By Dobri
The LPW heuristic is just another empirical...

The LPW heuristic is just another empirical observation based on the limited sample size.
There is an alternative interpretation for the graph of log2(log2(Mn)) versus n.
Perhaps another line with...
Forum: Dobri 2021-07-13, 22:35
Replies: 49
Views: 3,012
Posted By Dobri
Indeed, there is definitely something to reach...

Indeed, there is definitely something to reach for in this Mersennery game. Happy hunting, retina. :)
One could go wild and select digit sum 35 for manual testing, but preferably not if the test on...
Forum: Dobri 2021-07-13, 22:04
Replies: 49
Views: 3,012
Posted By Dobri
Applied statistics is not just a science but also...

Applied statistics is not just a science but also an art. When one attempts to estimate what would be the next Mersenne prime on the basis of the current small sample size of known Mersenne primes,...
Forum: Dobri 2021-07-13, 17:11
Replies: 49
Views: 3,012
Posted By Dobri
Post Digit sum of a Mersenne-prime exponent

The base-10 digit sums of the Mersenne exponents for the 51 known Mersenne primes are as follows:


2, 3, 5, 7, 4, 8, 10, 4, 7, 17, 8, 10, 8, 13, 19, 7, 13, 13, 14, 13, 32, 23, 8, 29, 11, 16, 28,...
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