Why do I get ~332M work assigned to the 100M search?

heliosh · 2017-10-02, 13:33

Hi,

I'm new to GIMPS and I have a question: When I sign up for the 100M-digit search, I get a 332M exponent. Why doesn't the search start by default at 100M?

And an OT question: How much performance do I lose if I run 1 worker +3 helper threads vs. 4 workers on a 4 core Haswell i5-4690K?

Batalov · 2017-10-02, 14:47

Try a simple calculation on your pocket calculator:
- Do 2*2*2*...*2 (10 times). That's 2¹⁰. How many digits does the answer have?
- Then do 2*2*2*...*2 (33 times). That's 2³³. How many digits does the answer have?

Now, observe that if you do the same 100M times and 332M times, you will get answers 10M times larger. See?

Madpoo · 2017-10-02, 15:04

Quote:

Originally Posted by heliosh

Hi,

I'm new to GIMPS and I have a question: When I sign up for the 100M-digit search, I get a 332M exponent. Why doesn't the search start by default at 100M?

And an OT question: How much performance do I lose if I run 1 worker +3 helper threads vs. 4 workers on a 4 core Haswell i5-4690K?

The simple answer is that "100M" refers to the # of decimal digits, but "332M" refers to an exponent in the range of 332,000,000 or more, which, as Batalov kind of points out, 2^332,000,000-1 (I'm approximating, don't give me any grief

) will have over 100 million decimal digits.

Maybe it's confusing to a newcomer to casually talk about 100M and 332M without knowing just what those #'s represent, but you definitely came to the right place to ask.

Hope that helps.

heliosh · 2017-10-02, 15:54

Ah thank you, it's clear now.

ATH · 2017-10-02, 16:08

Log₂(10^100,000,000) = log₁₀(10^100,000,000) / log₁₀ 2 = 100,000,000 / log₁₀ 2 ~ 100,000,000 / 0,301030 ~ 332,192,809

M344587487 · 2017-10-02, 16:45

I know it's been answered 3 different ways already, but this may be clearer: The >100M digit search refers to the number of decimal digits (probably coined because of the EFF prize), with 332M you're referring to the number of binary digits the exponent has.

Not to discourage you from doing what you want, but are you planning to do an LL test in the 100M range? If you've never done an LL test on the current wavefront, I suggest you try that first. Most people don't attempt or complete a 100M LL test because they take a very long time, and they're prone to fail even if taken to completion because of their length. Steps can be taken to mitigate a failed run (like ECC RAM or running the same test simultaneously, cross-checking as you go), but you'd have to be around a little while to know that.

Uncwilly · 2017-10-02, 18:22

We do have some contextually important shorthand around here.

M7 can refer to
M(7), that is 2⁷-1 with M() standing for the Mersenne function.
or
The seventh known Mersenne prime. This is the usual usage for numbers under 100. The parenthesis are used to clarify normally.

79.3M, 332M, etc. normally refers to exponent range (with M standing in for million): 2^79,300,000 -1
However, if you see 1M, 10M, or 100M, that will most often refer to the Mersenne numbers that have a decimal expression in the 1, 10, or 100 million digit range. This usage is almost only used for these 3.
If you see 70M or 90M and 100M used in the same discussion it will most likely mean the size of the exponent.

2017-10-02, 13:33	#1
heliosh Oct 2017 ++41 125₁₀ Posts	Why do I get ~332M work assigned to the 100M search? Hi, I'm new to GIMPS and I have a question: When I sign up for the 100M-digit search, I get a 332M exponent. Why doesn't the search start by default at 100M? And an OT question: How much performance do I lose if I run 1 worker +3 helper threads vs. 4 workers on a 4 core Haswell i5-4690K?

2017-10-02, 18:22	#7
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2³×1,223 Posts	We do have some contextually important shorthand around here. M7 can refer to M(7), that is 2⁷-1 with M() standing for the Mersenne function. or The seventh known Mersenne prime. This is the usual usage for numbers under 100. The parenthesis are used to clarify normally. 79.3M, 332M, etc. normally refers to exponent range (with M standing in for million): 2^79,300,000 -1 However, if you see 1M, 10M, or 100M, that will most often refer to the Mersenne numbers that have a decimal expression in the 1, 10, or 100 million digit range. This usage is almost only used for these 3. If you see 70M or 90M and 100M used in the same discussion it will most likely mean the size of the exponent. Last fiddled with by Uncwilly on 2017-10-02 at 18:24

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2017-10-02, 14:47	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2504₁₆ Posts	Try a simple calculation on your pocket calculator: - Do 222...2 (10 times). That's 2¹⁰. How many digits does the answer have? - Then do 222...2 (33 times). That's 2³³. How many digits does the answer have? Now, observe that if you do the same 100M times and 332M times, you will get answers 10M times larger. See?

2017-10-02, 15:54	#4
heliosh Oct 2017 ++41 175₈ Posts	Ah thank you, it's clear now.

2017-10-02, 16:08	#5
ATH Einyen Dec 2003 Denmark 3⁵×13 Posts	Log₂(10^100,000,000) = log₁₀(10^100,000,000) / log₁₀ 2 = 100,000,000 / log₁₀ 2 ~ 100,000,000 / 0,301030 ~ 332,192,809

2017-10-02, 16:45	#6
M344587487 "Composite as Heck" Oct 2017 814₁₀ Posts	I know it's been answered 3 different ways already, but this may be clearer: The >100M digit search refers to the number of decimal digits (probably coined because of the EFF prize), with 332M you're referring to the number of binary digits the exponent has. Not to discourage you from doing what you want, but are you planning to do an LL test in the 100M range? If you've never done an LL test on the current wavefront, I suggest you try that first. Most people don't attempt or complete a 100M LL test because they take a very long time, and they're prone to fail even if taken to completion because of their length. Steps can be taken to mitigate a failed run (like ECC RAM or running the same test simultaneously, cross-checking as you go), but you'd have to be around a little while to know that.