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 2014-10-16, 17:02 #1 isaac   "Isaac" Jul 2014 Israel 68 Posts back to the drawing board?! hi guys i don't know where to post this question/check i tested something on my computer and it seems that 22147483647-1 is prime its a every large number that ends with ...........3347 can anyone recheck my work please
2014-10-16, 17:23   #2
science_man_88

"Forget I exist"
Jul 2009
Dartmouth NS

204028 Posts

Quote:
 Originally Posted by isaac hi guys i don't know where to post this question/check i tested something on my computer and it seems that 22147483647-1 is prime its a every large number that ends with ...........3347 can anyone recheck my work please
Quote:
 Originally Posted by http://en.wikipedia.org/wiki/Double_Mersenne_number Double Mersenne primes A double Mersenne number that is prime is called a double Mersenne prime. Since a Mersenne number Mp can be prime only if p is prime, (see Mersenne prime for a proof), a double Mersenne number M_{M_p} can be prime only if Mp is itself a Mersenne prime. The first values of p for which Mp is prime are p = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127. Of these, M_{M_p} is known to be prime for p = 2, 3, 5, 7. For p = 13, 17, 19, and 31, explicit factors have been found showing that the corresponding double Mersenne numbers are not prime. Thus, the smallest candidate for the next double Mersenne prime is M_{M_{61}}, or 22305843009213693951 − 1. Being approximately 1.695×10694127911065419641, this number is far too large for any currently known primality test. It has no prime factor below 4×1033.[2] There are probably no other double Mersenne primes than the four known.[1][3]
from the wiki so 2^(2^31-1)-1 or 2^2147483647-1 has known factors:

Quote:
 Originally Posted by http://www.doublemersennes.org/factors.php?id=anno MM(31) Factor : 295,257,526,626,031
for example.

Last fiddled with by science_man_88 on 2014-10-16 at 17:25

 2014-10-16, 17:33 #3 isaac   "Isaac" Jul 2014 Israel 2·3 Posts thanks a lot! back to the drawing board i guess :)
 2014-10-16, 18:00 #4 CRGreathouse     Aug 2006 22×3×499 Posts What caused you to say that it was prime?
2014-10-16, 18:04   #5
TimSorbet
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"Tim Sorbera"
Aug 2006
San Antonio, TX USA

102678 Posts

Quote:
 Originally Posted by isaac 22147483647-1 is prime its a every large number that ends with ...........3347
Actually, it ends with 3327.

 2014-10-16, 19:20 #6 Primeinator     "Kyle" Feb 2005 Somewhere near M52.. 16268 Posts The post's headline made me very excited when I saw "new prime" on the main page under lounge. I go back to my day slightly more depressed. Also...is any computer currently even capable of testing an exponent of that size in a "reasonable" amount of time? Last fiddled with by Primeinator on 2014-10-16 at 19:22
2014-10-16, 19:55   #7
henryzz
Just call me Henry

"David"
Sep 2007
Liverpool (GMT/BST)

10111111101002 Posts

Quote:
 Originally Posted by Primeinator The post's headline made me very excited when I saw "new prime" on the main page under lounge. I go back to my day slightly more depressed. Also...is any computer currently even capable of testing an exponent of that size in a "reasonable" amount of time?
The best a 100M exponent can be done in it ~120 days on 4 cores. A 2000M exponent would take ~20^2=~400 times as long I think. So 100 years...

2014-10-16, 20:10   #8
TimSorbet
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

11×389 Posts

Quote:
 Originally Posted by Primeinator Also...is any computer currently even capable of testing an exponent of that size in a "reasonable" amount of time?
M595999993 on 3 or 4 threads of an AVX-capable CPU takes about 4.25 days for 5M iterations, or about 507 days.

M345678877 on a Black-Titan takes about 59 days of crunching.

Each time you double p, you roughly quadruple the run time. (double the iterations, double the time per iter, roughly)
2^1.85*596M ~= 2^31. So MM31 is about (4^1.85=)13 times harder, or would take (507 days * 13=)18 years on that CPU.
2^2.635*345.7M ~= 2^31. (4^2.635=)38.6 times harder, or would take 6.23 years on that GPU. The Titan Z (which is the best on this list) is faster than the Titan Black, taking about 63% of the time to do a given task. That would still take close to 4 years of running 24/7.

I'd say 4 years on a GPU is a little outside of a "reasonable" amount of time, leaving aside questions like "is there even software that can run that on a GPU?" and "does the GPU in question have enough memory?".

Luckily, the realistic answer to all this is, we've already eliminated the need to test this by finding factors!

Last fiddled with by TimSorbet on 2014-10-16 at 20:19

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