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Old 2019-04-03, 17:39   #12
greenskull
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One more interesting topic.

This is the plot that shows us the number of days (y axis) since 09 February 1997 (starting poin x=0, y=0) when all tests below chosen exponent (x axis) have been verified.
https://ibb.co/2nbJs29

I took the data from here:
https://www.mersenne.org/report_milestones
I calculated the starting point 09 February 1997 (x=0, y=0) in such a way that the curve data approximation gave the smallest error.

This mathematical function allows us to extrapolate the day (since 09 February 1997) for any exponent (x axis) when all tests below it will be verified.
At the last 10 values, the error is quite small and does not exceed on average Β±45 days. Although of course the value can walk in the larger tube of error.
I wrote about it here:
https://www.mersenneforum.org/showpo...postcount=3072

We could estimate that all tests below M57885161 will be completed on 12 September 2021 Β±45 days.
https://ibb.co/b11f3tt

Assuming the validity of my hypothesis, it can be assumed that at least 3 new Mersenne Prime numbers will be open by this date.
But there are no guarantees and of course not limited to this interval :)
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Old 2019-04-03, 17:54   #13
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Quote:
Originally Posted by ATH View Post
Good luck with your hypothesis, I would not bet any money on it if I were you. We will see in a few years who was correct.

I bet on 0 or 1 new prime in the interval 43112609 to 82589933, but most likely 0.
Betting against looks like easy money.
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Old 2019-04-03, 18:16   #14
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Quote:
Originally Posted by ATH View Post
Good luck with your hypothesis, I would not bet any money on it if I were you. We will see in a few years who was correct.

I bet on 0 or 1 new prime in the interval 43112609 to 82589933, but most likely 0.
My calculations say there are 10..15 new Mersenne Primes. It sounds crazy I know.

But if we assume that there is only 1 new number, then it will look like this (orange line):
https://ibb.co/X4pMdyx

From my point of view it does not look very organic.
But I will not argue, sure you could be right, time will tell.

Last fiddled with by greenskull on 2019-04-03 at 18:24
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Old 2019-04-03, 18:29   #15
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Quote:
Originally Posted by knowhow View Post
My calculations say there are 10..15 new Mersenne Primes. It sounds crazy I know.
Is there any chance your calculations are incorrect?
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Old 2019-04-03, 18:42   #16
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Quote:
Originally Posted by chalsall View Post
Is there any chance your calculations are incorrect?
50/50 -- it may or may not be correct :)
But seriously speaking, it all comes down to a smooth approximation of the Cumulative amount of Mersenne Primes on the interval M3021377..M43112609 and reliable extrapolation behind this interval.
Everything else is not contradictive, you see all the explanations to the idea.
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Old 2019-04-03, 18:51   #17
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The only case that I know of a Mersenne prime found out of order (and not by just 10 months like M42643801) it is Mp110503 by Colquitt & Welsh -on January 1988-

We need to make note, however, that this was before GIMPS which started 8 years later in January 1996.

Mp132049 and Mp216091 where discovered before M110503, on Sept. '83 and Sept. '85 respectively.

As far as I know when Colquitt and Welsh found 2110,503-1 to be prime, the search up to exponent 216,000 was _not_ exhaustive.

So this was not the case (someone correct me if I'm wrong) of an exponent being check the first time and found composite by mistake and then discovered in a DC to be prime.
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Old 2019-04-03, 19:06   #18
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Quote:
Originally Posted by knowhow View Post
50/50 -- it may or may not be correct :)
But seriously speaking, it all comes down to a smooth approximation of the Cumulative amount of Mersenne Primes on the interval M3021377..M43112609 and reliable extrapolation behind this interval.
Everything else is not contradictive, you see all the explanations to the idea.
I think Caldwell's exposition of the math contradicts your approach.
There's no reason to think that sequence number versus p of the sorted Mp series should be a smooth function, and there are adjacent Mps that show it is not.
Quote:
From my point of view it does not look very organic.
You seem there to be substituting esthetic judgment for logic. Graphing the most likely scenario would assume zero undiscovered Mp below M82589933, and go through M47 not M46.

Last fiddled with by kriesel on 2019-04-03 at 19:23
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Old 2019-04-03, 19:36   #19
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Quote:
Originally Posted by kriesel View Post
There's no reason to think that sequence number versus p of the sorted Mp series should be a smooth function, and there are adjacent Mps that show it is not.
I do not mind. But if you carefully look at the Cumulative amount of Mersenne Primes curve over the entire interval up to M43112609, you will see that it is pretty smooth. There is no reason to believe that this smoothness will suddenly break after M43112609. The curve can wag slightly, but not sharply, but smoothly. That, what I call it looks organic.
I mean Cumulative amount of Mersenne Primes, not any others.

I have no claim to absolute truth, I laid out some ideas, and described how I came to it. Time will show everything.
Maybe I will make a couple more clarifications when I have new thoughts.
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Old 2019-04-04, 00:27   #20
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Quote:
Originally Posted by knowhow View Post
...the Cumulative amount of Mersenne Primes curve over the entire interval up to M43112609, you will see that it is pretty smooth.
True. Irrelevant. The smoothness is an artifact unavoidably introduced by the process of fitting a continuous curve to discrete data. The curve is not the data, it is an approximation. The smoothness is a property of the form of the approximation, and not of the data.

As a former employer was fond of saying, the map is not the territory. We know the data has steps in it. It is a staircase with vertical increments of one. Graph # of known Mp below x, versus p, from M47. It's the same value, 47, from 43112609, all the way up to at least https://www.mersenne.ca/exponent/46769119, and probably to 57885143 or 57885160.
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Old 2019-04-04, 07:52   #21
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Quote:
Originally Posted by retina View Post
So it would seem your "hidden" numbers are really just numbers we already know about and have already tested as composite, but you are claiming are prime. Is that what you mean?
https://en.wikipedia.org/wiki/Great_...ied_index^_†
Quote:
^ † As of March 29, 2019, 46,753,351 is the largest exponent below which all other prime exponents have been checked twice, so it is not verified whether any undiscovered Mersenne primes exist between the 47th (M43112609) and the 51st (M82589933) on this chart; the ranking is therefore provisional. Furthermore, 83,032,877 is the largest exponent below which all other prime exponents have been tested at least once, so all Mersenne numbers below the 51st (M82589933) have been tested.
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Old 2019-04-04, 08:27   #22
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Quote:
Originally Posted by knowhow View Post
https://en.wikipedia.org/wiki/Great_...ied_index^_†
Quote:
^ † As of March 29, 2019, 46,753,351 is the largest exponent below which all other prime exponents have been checked twice, so it is not verified whether any undiscovered Mersenne primes exist between the 47th (M43112609) and the 51st (M82589933) on this chart; the ranking is therefore provisional. Furthermore, 83,032,877 is the largest exponent below which all other prime exponents have been tested at least once, so all Mersenne numbers below the 51st (M82589933) have been tested.
Why are you quoting stuff we all already know? What we still don't know is what you mean by "hidden numbers"?
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