Mersenne prime exponent not randomly distributed? - Page 6

ewmayer · 2013-02-05, 01:50

The 2 sort-predicates need to occur at top of their containing .c file, otherwise the compiler needs separate declarations-in-a-header.

#define HERE __LINE__, __FILE__

R. Gerbicz · 2013-02-05, 04:19

[k*10^6-40000,k*10^6+40000] (with integer k) is true for Mersenne exponents with index from 36 to 42 the only exception is p=13,466,917. This is also interesting.

ewmayer · 2013-02-05, 18:05

B -smoothness: 57885161 is 69 of 1140, percentile = 94.04
S_{L[sup]2[/sup]}-smoothness: 57885161 is 135 of 1140, percentile = 88.25

ewmayer · 2013-02-05, 18:19

Summary table:

Code:

p			B -smooth	L2-smooth
--------		---------	---------
110503			47.31		56.85
132049			78.57		93.15
216091			99.88		97.62
756839			28.72		17.03
859433			88.34		78.98
1257787			20.32		26.56
1398269			 5.42		 5.42
2976221			41.08		49.67
3021377			57.65		86.36
6972593			91.83		87.35
13466917		62.51		71.26
20996011		99.75		99.16
24036583		 8.03		 8.03
25964951		73.05		77.42
30402457		98.74		94.44
32582657		87.41		99.32
37156667		55.44		39.93
42643801		97.02		98.64
43112609		54.13		85.28
57885161		94.04		88.25

Average:		64.46		68.04

So, if you had a family with 20 children of various ages - "you may be eligible for a papal certificate of fecundity and outstanding contribution to global overpopulation! See details below on how to apply" - and of heights of the above percentiles with respect to their same-age cohort, would you be justified in concluding that this family taken as a whole has children taller than average, in a statistically significant fashion?

Also note, 6 of 20 for each smoothness measure in the > 90%ile range, and half of those are 99%ers.

Dubslow · 2013-02-05, 18:22

I have to point out we haven't even examined what "average" is yet. (That is, what's the distribution for all the 1000s of primes in a range around an MP expo? Is it a bell curve...?)

ewmayer · 2013-02-05, 18:28

Quote:

Originally Posted by Dubslow

I have to point out we haven't even examined what "average" is yet. (That is, what's the distribution for all the 1000s of primes in a range around an MP expo? Is it a bell curve...?)

That would be an excellent use of the standalone code you pieced together from the files I sent you, plus some plotting magic.

Dubslow · 2013-02-05, 18:35

Quote:

Originally Posted by ewmayer

That would be an excellent use of the standalone code you pieced together from the files I sent you, plus some plotting magic.

Except for the problem of qsort apparently crashing for no reason at all

My plan is to reimplement it in Python, which will be a lot slower but also very little code and effort on my part. Unfortunately I've distracted myself all morning reading about hacking python

Batalov · 2013-02-05, 18:42

- get a sample (set of numbers)
- run t-tests
- apply FWER correction (Holm-Bonferroni, Benjamini-Hochberg, take your pick)
- ?????
- PROFIT!

ewmayer · 2013-02-05, 19:36

Quote:

Originally Posted by Dubslow

Except for the problem of qsort apparently crashing for no reason at all

Why don't you post the current codebase here, along with your platform/build-setup, for others with similar systems to try.

Since it works fine for me (built using gcc 4.2 under Mac OS), I can't be of much help here.

Dubslow · 2013-02-05, 19:40

Quote:

Originally Posted by ewmayer

Why don't you post the current codebase here, along with your platform/build-setup, for others with similar systems to try.

Since it works fine for me (built using gcc 4.2 under Mac OS), I can't be of much help here.

Well since my "codebase" is meant to be independent of your local setup, you still still try it in its own folder.

To anyone willing to try it: it should compile out of the box with `gcc -Wall mprime_exp_smooth. -o mpsmooth -lm`, and try running `./mpsmooth`. For me it crashes in the sort before even calling any comparison functions (which are the only code I added).

Dubslow · 2013-02-05, 22:11

Wow, my Python is slow

it takes 5-10 seconds to process M110503. I'll edit in some results soon.

Edit: Well, I made at least one stupid, but that doesn't appear to have solved the problem. Still getting crashes with a fixed compare.

2013-02-05, 18:19	#59
ewmayer ∂²ω=0 Sep 2002 República de California 19×613 Posts	Summary table: Code: p B -smooth L2-smooth -------- --------- --------- 110503 47.31 56.85 132049 78.57 93.15 216091 99.88 97.62 756839 28.72 17.03 859433 88.34 78.98 1257787 20.32 26.56 1398269 5.42 5.42 2976221 41.08 49.67 3021377 57.65 86.36 6972593 91.83 87.35 13466917 62.51 71.26 20996011 99.75 99.16 24036583 8.03 8.03 25964951 73.05 77.42 30402457 98.74 94.44 32582657 87.41 99.32 37156667 55.44 39.93 42643801 97.02 98.64 43112609 54.13 85.28 57885161 94.04 88.25 Average: 64.46 68.04 So, if you had a family with 20 children of various ages - "you may be eligible for a papal certificate of fecundity and outstanding contribution to global overpopulation! See details below on how to apply" - and of heights of the above percentiles with respect to their same-age cohort, would you be justified in concluding that this family taken as a whole has children taller than average, in a statistically significant fashion? Also note, 6 of 20 for each smoothness measure in the > 90%ile range, and half of those are 99%ers.

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2013-02-05, 01:50	#56
ewmayer ∂²ω=0 Sep 2002 República de California 19×613 Posts	The 2 sort-predicates need to occur at top of their containing .c file, otherwise the compiler needs separate declarations-in-a-header. #define HERE __LINE__, __FILE__

2013-02-05, 04:19	#57
R. Gerbicz "Robert Gerbicz" Oct 2005 Hungary 2×743 Posts	[k10^6-40000,k10^6+40000] (with integer k) is true for Mersenne exponents with index from 36 to 42 the only exception is p=13,466,917. This is also interesting.

2013-02-05, 18:22	#60
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 3×29×83 Posts	I have to point out we haven't even examined what "average" is yet. (That is, what's the distribution for all the 1000s of primes in a range around an MP expo? Is it a bell curve...?)

2013-02-05, 18:42	#63
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×47×101 Posts	- get a sample (set of numbers) - run t-tests - apply FWER correction (Holm-Bonferroni, Benjamini-Hochberg, take your pick) - ????? - PROFIT!