Oops - New Prime! (M49 related)

[ewmayer]

Originally Posted by Madpoo

The milestones page shows 81,788 exponents remaining to be first-time checked below M49.

If we further estimate that 5% of the 554,000 that need double-checking below M49 will be bad, that's another ~27,700 that we may as well treat as if they weren't done at all yet.

Thanks - so all but ~110,000 (i.e. roughly 90%) of the primes in the interval have already been taken out of consideration, thus my estimate drops to around 0.07 expected primes, which is even more pessimistic than Mini-Geek's.

[Mini-Geek]

Originally Posted by Batalov

All the bicycles are invented a long time ago, dudes...

# time ../pfgw64.exe -od -q"2^74207281-1" > M49
PFGW Version 3.7.9.64BIT.20141125.x86_Dev [GWNUM 28.7]

11.364u 0.220s 0:10.73 107.9%   0+0k 0+43648io 0pf+0w

@ wc  M49
       1        2 22338669 M49

# cut -c-50 M49
2^74207281-1: 300376418084606182052986098359166050

If you already know what number you want, that's nice (low effort). But it doesn't let you easily search in the whole 74M range for the right one: at 11 seconds per number (I'm assuming that searching the file to see if the hints match is trivial), with ~20,000 numbers, that's 2.5 CPU days.

I looked back over the thread, and realized I ignored a useful clue: that the exponent contains "42". That, along with parallelizing my code, cut the time down to 35 minutes. Then I found a list of exponents with known factors, that cut it down to 2689 candidates, which I can search in about 12 minutes.

Originally Posted by ewmayer

Using 906644 odd primes ...

You're including all primes, which isn't what I did. I used the stats at http://www.mersenne.org/primenet/ to try to take into account known factors and LLs (of the various kinds, and their accuracy: e.g. LL-D is sure, LL-ERR I counted as 50/50). So I think it's accurate to say that before we searched any, we should expect 0.683 in the range, but since we've LL'd the bulk of it, we only expect 0.18 more primes in the range.

(I used the (e^gamma/log 2) * log log x formula from your link, and took the simplification of assuming that all numbers in the range had equal probability to be prime; since more of the earlier ones were LL'd, that means my 0.18 is a bit of an overestimate...Edit: Didn't see your more recent post until now, I don't think it would account for the difference between 0.07 and 0.18, though; not sure about that)

[ixfd64]

Does anyone know how much faster GPU to 72 allowed us to find this new prime?

[Jayder]

I am considering getting a book printed of the decimal expansion of M74207281. It's not a poster, but it's probably the next best thing. lightningsource.com (the only publisher I found that supports books over 800 pages) gives a quote of $29.54 USD (plus shipping) for a 1200 page hardcover. I haven't looked past their quote calculator, so I'm not sure if they would be too happy about printing a book like this with no author or words and at a smaller font size (at most 5.5).

[retina]

Originally Posted by Jayder

I am considering getting a book printed of the decimal expansion of M74207281. It's not a poster, but it's probably the next best thing. lightningsource.com (the only publisher I found that supports books over 800 pages) gives a quote of $29.54 USD (plus shipping) for a 1200 page hardcover. I haven't looked past their quote calculator, so I'm not sure if they would be too happy about printing a book like this with no author or words and at a smaller font size (at most 5.5).

You could make it cheaper by not printing the middle 95% of the pages, just leave them blank. Considering that people will only look at the start and the end digits they will never notice that the middle pages are all blank.

[axn]

Auto translated?

[LaurV]

Originally Posted by axn

Auto translated?

Haha, Emmett Brown? Looks more like Emelius Browne..

[0PolarBearsHere]

Originally Posted by ixfd64

Does anyone know how much faster GPU to 72 allowed us to find this new prime?

It looks like it was TFed to 75 bits, not sure how much was via GPUto72 though. Chris should be able to tell us.
http://www.mersenne.ca/exponent.php?...tails=74207281

[0PolarBearsHere]

Originally Posted by 0PolarBearsHere

It's currently in the slashdot firehose as red, so it might be hitting the front page soon.

Now on the front page of slashdot
http://science.slashdot.org/story/16...-274207281---1

[ATH]

Originally Posted by ewmayer

I use my own code to generate the decimal printouts - still way slower than it could be, took ~3 hours on 1 cpu of my 2GHz Core2Duo macbook classic, probably at least 100x slower than it could be

Piping the output of this into a file took 6 sec:

#include <gmp.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <math.h>

void main()
{
    mpz_t s;
    mpz_init_set_ui(s,0);
    mpz_ui_pow_ui(s,2,74207281); mpz_sub_ui(s,s,1);
    gmp_printf("%Zd",s);
}

[0PolarBearsHere]

Originally Posted by ATH

Piping the output of this into a file took 6 sec:

5->7 minutes to get the right libraries compiled and installed, 5 minutes to fix an error in my command line, 4.5 seconds to run the code haha (followed by a few minutes to download the zip file from the server, extract it, and strip the white space to do a diff).