Reference material discussion thread

[kriesel]

This is where I'd prefer the reference material be publicly discussed. (Not in the reference material threads themselves.)

[Uncwilly]

You are doing an important job.

[ET_]

Originally Posted by kriesel

What's the exponent required for 10, 100 or 1000 megadigit Mersenne primes?
How was that calculated?

Also included is a rough ballpark estimate of what's feasible on a GTX1070 in CUDALucas 2.06beta.

33,219,283 , 332,192,831 and 3,321,928,097 respectively.

[LaurV]

Originally Posted by kriesel

How was that calculated?

Logarithms. I won't repeat what ET said, but just use the logarithms properties to compute the binary logarithm of 10 at the power 1M (the first number with 1M decimal digits), considering that \(\log_a x^n=n\log_a x\) and \(\log_a x=\frac{log_b x}{log_b a}\).


To calculate how many digits in base 5 will \(10^{1000000}\) have, you need to compute \(\log_5 10^{1000000}\).
To calculate how many bits will \(10^{1000000}\) have, you need to compute \(\log_2 10^{1000000}\). That is the power of 2 you need to raise 2 to get 10^1M (i.e a number with 1M digits). Then round it to the next prime.

[axn]

Originally Posted by LaurV

To calculate how many digits in base 5 will \(10^{1000000}\) have, you need to compute \(\log_5 10^{1000000}\).
To calculate how many bits will \(10^{1000000}\) have, you need to compute \(\log_2 10^{1000000}\). That is the power of 2 you need to raise 2 to get 10^1M (i.e a number with 1M digits). Then round it to the next prime.

But keep also in mind that 10^1000000 has 1000001 digits, and 10^999999 has 1000000 digits.

[kriesel]

Originally Posted by Uncwilly

You are doing an important job.

Thanks!

Try as I might, I can not get those two lincolns from the screen to my pocket ;)

(That's not why I'm doing this. When joining the gpu Mersenne hunting effort a little over a year ago, I looked for reference material and found less than I expected. What I found was scattered about. Made my own for my own use, and figured I might as well share and save someone else some time or puzzlement or wasted cycles. And feedback from doing so could help enlighten me; win-win.)

[kriesel]

The posts #3-5 above are moved here and were in reference to http://www.mersenneforum.org/showpos...4&postcount=11.
At this point there's been only one view of the attachment to that post, which is what my rhetorical questions were intended as the setup for. (I've modified that post's text a bit to be hopefully more clear about that.)

Some nice posts, thoughtful, well formatted; I just don't want them in the reference thread, so they're relocated to here.

Are people reluctant to view attachments for some reason, or pdfs in particular? If so, why? Do you prefer other attachment types? Some way of inlining the content? Do attachments not show up as available in some browsers? What would you recommend or prefer?

[kriesel]

Originally Posted by axn

But keep also in mind that 10^1000000 has 1000001 digits, and 10^999999 has 1000000 digits.

Good point, and part of why I originally included two columns in the quick reference table in the attachment, the lowest and highest integer exponents for Mersenne numbers to have precisely 10ⁿ digits, vs. 10ⁿ values, n=1,2,..10.
10^{10^6} has 10⁶+1 decimal digits, but 10^{10^6}-1 has 10⁶, as does 10^{10^6}/9.99 or 10^{10^6}/8.
I just now checked the cell formulas in the underlying spreadsheet against http://oeis.org/A034887 which covers2^p, p=0,1,...72.

Originally Posted by kriesel

Some things to check if the system uptime or other reliability is less than quite good.

1. How old is the hardware? (Hard drive etc not too ancient? All components and connectors well seated and making good contact?)
2. Recent backups, running on schedule, well monitored to ensure they're actually running to completion?
3. How well patched is the system?
4. How well is it protected from power interruption or transients or sags? (Voltage regulating UPS?)
5. Do you have a way of monitoring the line voltage?
6. What do system logs have to say?
7. How detailed and complete is your system logging? (Is some logging going to another system or storage device? Will it survive a HD problem in the system of interest?)
8. What OS is it running?
9. What other software?
10. Is it safe from children and other small animals?
11. System components and memory pass reliability tests? What if anything does/would a serious diagnostics attempt tell you? https://lifehacker.com/5551188/best-...agnostic-tools
12. What assumptions are you making and may not even realize it?
13. Temperature of components and ambient environment in a reasonable range?
14. Relative humidity in a reasonable range?
15. All fans in the system in good working order? Grilles and components free of dust, lint, and pet hair?
16. A full complement of drivers, of reliable versions, typically up to date except for recent releases with known issues?
17. Well secured?
18. Correct power supply output voltages, and adequate current output for all the components now installed on all voltage levels? System components get added, and power supply components degrade over time. Wattage required varies with operating temperature, clock rate, program execution, etc.

I'd say that you have to upgrade the bios as well.

[kriesel]

Originally Posted by SELROC

I'd say that you have to upgrade the bios as well.

Thanks, added. Also modified the other one you commented on.

[LaurV]

Originally Posted by axn

But keep also in mind that 10^1000000 has 1000001 digits, and 10^999999 has 1000000 digits.

Haha, I think it is the second time when you catch me with this...
Anyhow, it is irrelevant, because log(10,2) is 3.32192809488736 and when you multiply it with either 10M or 10M-1, you get 33219280.xx and 33219277.xx, respectively, and there is no prime in between. The next prime candidate for the exponent is (as ET already said) 33219283 (which has 10M+2 digits, probably).