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Old 2021-05-17, 23:30   #1
drkirkby
 
"David Kirkby"
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Default Is there an accepted standard for refering to Mersenne Prime numbers?

I'm a bit confused by what seems to be an inconsistent way of numbering Mersenne prime numbers. For example, is the 19th Mersenne prime (2^89 -1 = 618970019642690137449562111)

M10 - since it is the 10th one.
M(10) - since it is the 10th one.
M(89) - since the exponent is 89
M89 - since the exponent is 89
M6,189,70,019,642,690,137,449,562,111
M(6,189,70,019,642,690,137,449,562,111)

something else?

And how about Mersenne numbers which are not prime - eg 2^11 -1 = 2047 = 23*89 ?

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Old 2021-05-17, 23:38   #2
chalsall
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Quote:
Originally Posted by drkirkby View Post
I'm a bit confused by what seems to be an inconsistent way of numbering Mersenne prime numbers.
David. If I may please ask you a sincere question...

You seem to be a fairly smart person. You give enough information for us to be able to drill down and find you have a PhD.

And yet you seem to ask some very stupid questions. The question is... why do you do this?
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Old 2021-05-18, 00:42   #3
drkirkby
 
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Quote:
Originally Posted by chalsall View Post
David. If I may please ask you a sincere question...

You seem to be a fairly smart person. You give enough information for us to be able to drill down and find you have a PhD.

And yet you seem to ask some very stupid questions. The question is... why do you do this?
Yes, I do have a PhD, although the "dr" at the front of my username is actually my initials. My PhD is in medical physics and bioengineering.

I don't think the question is so stupid, as the literature is inconsistent on this. The terms don't seem to be used consistently on these forums

Here https://www.mersenneforum.org/showthread.php?t=23892
Uncwilly asks people to predict M52.

yet here,

https://www.mersenne.ca/exponent/103750501
in the top left, we see M103750501, and read further down "No known factors for M103,750,501"

So there are two conflicting examples of representing the numbers. I have seen others too.

In cases the context makes it fairly obvious, but M17 could refer to 2^17 -1 or the 17th Mersenne Prime which is 2^2381 -1.

Here, parentheses are used.

https://www.math.wichita.edu/history/men/mersenne.html
it says "Currently GIMPS is checking and double checking to verify (prove) that M(6972593) is indeed the 38th Mersenne Prime."


So that's 3 different ways. Perhaps I just have to accept the inconsistency, but I would not expect that from mathematicians.

Dave

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Old 2021-05-18, 01:04   #4
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Quote:
Originally Posted by drkirkby View Post
So that's 3 different ways. Perhaps I just have to accept the inconsistency, but I would not expect that from mathematicians.
The confusion is generally only for numbers 1 to 100. If you see any number greater than 100 you can expect it to be 2p-1 vs. the pth. That is also generally the case for numbers a little above the current record holder. Another rule of thumb, if you see a number that is not prime, you can expect it to be referring to the pth known Mersenne Prime. So in most cases, you can tell by context. There are some folks that also use XXM as opposed to MXX to distinguish numbers.

Also, a rule of thumb is to check the wiki to find answers for questions like this.
Also, there is not a big need for excessive blank lines in posts.
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Old 2021-05-18, 01:08   #5
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Quote:
Originally Posted by drkirkby View Post
I'm a bit confused by what seems to be an inconsistent way of numbering Mersenne prime numbers. For example, is the 19th Mersenne prime (2^89 -1 = 618970019642690137449562111)
<snip>
The notation is ambiguous, but the intended meaning can be inferred easily from context; not merely "in cases," but in every case I'm aware of. At least, if you're aware of the notational ambiguity.

A similar situation exists with "repunit" numbers (10k - 1)/9. Rn can mean the nth repunit prime (or probable prime), as in a graph posted to a recent thread. But in a statement like "R8177207 is a PRP" the subscript clearly means the exponent.
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Old 2021-05-18, 02:25   #6
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There's a simple way to avoid or reduce the ambiguity. See https://www.mersenneforum.org/showpo...67&postcount=4
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Old 2021-05-18, 07:37   #7
drkirkby
 
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Quote:
Originally Posted by Uncwilly View Post
The confusion is generally only for numbers 1 to 100. If you see any number greater than 100 you can expect it to be 2p-1 vs. the pth. That is also generally the case for numbers a little above the current record holder. Another rule of thumb, if you see a number that is not prime, you can expect it to be referring to the pth known Mersenne Prime. So in most cases, you can tell by context. There are some folks that also use XXM as opposed to MXX to distinguish numbers.

Also, a rule of thumb is to check the wiki to find answers for questions like this.
I appreciate for large numbers > 100, the number will be the exponent. But for an example I gave of 17, it is far from obvious. However, I was looking for a formula to write a sequence to OIES. In that case, I ideally would have used the most commonly used method. (Obviously I looked what was used on OIES too). Either way, it looks like one needs to explain ones meaning more than one would for factorial, sin, cos etc.

I think the comment from chalsall that this was a very stupid question is a little unfair, but he/she is entitled to their opinion.

As to the spaces, whenever I write a post on here, extra spaces get added. Unusually I remove them in the preview, or immediately go back and edit the post. I get the same problem whether I use Firefox on Windoze, Linux or Solaris. I must have omitted to do both in this case.

Dave
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Old 2021-05-18, 07:56   #8
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Quote:
Originally Posted by drkirkby View Post
In cases the context makes it fairly obvious, but M17 could refer to 2^17 -1 or the 17th Mersenne Prime which is 2^2381 -1.
Mp#17 = 22281-1.

For more clarity, we would use Mx for 2x-1, Mpy=yth Mersenne prime, or Mpy=Mx. But due to past practice, using Mx for both xth and 2x-1, Mx is inconveniently ambiguous for x<~53 at the moment, x prime, 2x-1 prime; 2 3 5 7 13 17 19 31, 8 cases. Writing "Mp2=M(3)" where M(x) = f(x) =2x-1 could help. Or perhaps Mp#2 = M3 = 7; Mn11=2047. Mp#x concisely abbreviates "Mersenne prime number" x, signifying position in the list of known Mersenne primes. The usual convention is to follow with an asterisk, those that are not verified up to, as Mp48* - Mp51*. https://www.mersenne.org/primes/
There's value to readers in writing clearly enough once, that numerous readers needn't think much to disambiguate what's written, every time it's read, and not assuming or requiring as much prior knowledge. We do occasionally get total noobs here on the forum, who've just learned of Mersenne numbers, and are reading here out of curiosity.

The extra-line-breaks phenomenon/nuisance began sometime after 2016. It did not occur when I first joined in early 2017. A habit to use Advanced Edit, and Preview Changes always, helps. It appears to be a Firefox related issue; MS Edge does not have it, based on a very brief test.

OEIS has https://oeis.org/A000668 (Mersenne primes) and https://oeis.org/A000043 (exponents of Mersenne primes)

Last fiddled with by kriesel on 2021-05-18 at 08:57
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Old 2021-05-18, 10:56   #9
charybdis
 
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Quote:
Originally Posted by drkirkby View Post
However, I was looking for a formula to write a sequence to OIES. In that case, I ideally would have used the most commonly used method. (Obviously I looked what was used on OIES too). Either way, it looks like one needs to explain ones meaning more than one would for factorial, sin, cos etc.
On this forum, when someone writes something like "M51" or "M82589933" it is clear what is being referred to. That isn't the case in the wider mathematical community. For instance, a group theorist would have a very different idea of what M11 means. So for OEIS purposes, you should use "2^p-1" or "the n-th Mersenne prime" as appropriate.

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Old 2021-05-18, 12:29   #10
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Other options could be: M#52 or M52# or M52nd/M47th etc.
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Old 2021-05-18, 12:46   #11
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We like M83.

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