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[NBtarheel_33]

February 3, 2015 All exponents below 33,219,253 (10 million digits) double-checked.

Just because I'm feeling extra nitpicky this afternoon: 33,219,253 in the above should really be 33,219,281.

[Uncwilly]

Originally Posted by ATH

Checking the milestones list against some old status files:

Milestones graph: milestones.png

It seems that you have some data points on that that I don't have (2008 and 2009 especially.) Would you be willing to share what you have? I can PM you my e-mail address.

[Madpoo]

Originally Posted by NBtarheel_33

February 3, 2015 All exponents below 33,219,253 (10 million digits) double-checked.

Just because I'm feeling extra nitpicky this afternoon: 33,219,253 in the above should really be 33,219,281.

I thought the first 2^n-1 that resulted in 10M digits is n=33219280 (which isn't prime, but doesn't matter). 2^33,219,281 - 1 would have more than 10M digits, wouldn't it?

I don't remember where or how I came up with 33219280 as the magic number, but that's what I was using as a basis. I don't have the energy to double-check right now... past my bedtime.

[Madpoo]

Originally Posted by Uncwilly

It seems that you have some data points on that that I don't have (2008 and 2009 especially.) Would you be willing to share what you have? I can PM you my e-mail address.

Maybe I can look at the milestone list and double-check, add the missing n-millionth items and verify the ones listed. They're probably okay.

[axn]

Originally Posted by Madpoo

I thought the first 2^n-1 that resulted in 10M digits is n=33219280 (which isn't prime, but doesn't matter). 2^33,219,281 - 1 would have more than 10M digits, wouldn't it?

I don't remember where or how I came up with 33219280 as the magic number, but that's what I was using as a basis. I don't have the energy to double-check right now... past my bedtime.

All exponents below (I bolded, underlined & italicized for added effect )

[retina]

Originally Posted by axn

All exponents below (I bolded, underlined & italicized for added effect )

All exponents below (I bolded, underlined, italicised coloured & enbiggened for added effect )

[LaurV]

Originally Posted by Madpoo

I thought the first 2^n-1 that resulted in 10M digits is n=33219280 (which isn't prime, but doesn't matter). 2^33,219,281 - 1 would have more than 10M digits, wouldn't it?

I don't remember where or how I came up with 33219280 as the magic number, but that's what I was using as a basis. I don't have the energy to double-check right now... past my bedtime.

Actually if we are to be nitpicking...

gp > ceil(33219277*log(2)/log(10))
time = 1 ms.
%1 = 9999999
gp > ceil(33219278*log(2)/log(10))
time = 1 ms.
%2 = 10000000
gp > length(Str(1<<13-1))
%3 = 4
gp > length(Str(1<<14-1))
%4 = 5
gp > length(Str(1<<33219277-1))
time = 14,928 ms.
%5 = 9999999
gp > length(Str(1<<33219278-1))
time = 15,241 ms.
%6 = 10000000
gp > precprime(33219278)
time = 1 ms.
%7 = 33219253
gp > nextprime(33219278)
%8 = 33219281
gp >

(the log/ceil stuff is sometime tricky, if not enough precision in floats, here the precision is high enough, but usually "printing it" in a decimal string will resolve all the arguments, even if this is very slow, especially in pari/gp)

[retina]

Originally Posted by LaurV

(the log/ceil stuff is sometime tricky, if not enough precision in floats, here the precision is high enough, but usually "printing it" in a decimal string will resolve all the arguments, even if this is very slow, especially in pari/gp)

I would have thought the standard log function would suffice:

(10^7-1)/log10(2) = 33,219,277.62.....

And no more than 10 digits of precision needed.

The next decade is: (10^8-1)/log10(2) = 332,192,806.16...

[LaurV]

Originally Posted by retina

All exponents ʍo|ǝq (I bolded, underlined, italicised coloured & enbiggened uʍop ǝpısdn ʇı pǝddı|ɟ for added effect )

noʎ ɹoɟ ʇɐɥʇ pǝxıɟ...

[LaurV]

Originally Posted by retina

I would have thought the standard log function would suffice:

(10^7-1)/log10(2) = 33,219,277.62.....

And no more than 10 digits of precision needed.

The next decade is: (10^8-1)/log10(2) = 332,192,806.16...

Try: (10^7)/log10(2) = ?
(and then start thinking what happens with the exponents in between...)

[Madpoo]

Originally Posted by axn

All exponents below (I bolded, underlined & italicized for added effect )

I was confused what y'all were talking about, but I see now you're just being super precise (which I should appreciate, but I missed it).

So I should say "All exponents below *or equal to* blah blah have been double-checked"

I guess that's one thing in favor of using the language "up to" which is inclusive.

I'm looking at the milestone page and with all the stuff in there for the n-millionth stuff it's a little cluttered as time goes on, so maybe I'll try to organize it better... I'll make the change then.

FYI, looking at the database to try and figure out milestone dates is a little more daunting since triple-checks or other things are sometimes done, so I can't just look at the last date of a result in a certain exponent range. I'll have to do a little SQL magic to work out the actual date a single or double-check came in. The smaller exponents won't necessarily have that info in the v5 database either...maybe in the v4 database. :)