back to the drawing board?!

[isaac]

hi guys

i don't know where to post this question/check

i tested something on my computer and it seems that

2^2147483647-1 is prime

its a every large number that ends with ...........3347

can anyone recheck my work please

[science_man_88]

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

2^2147483647-1 is prime

its a every large number that ends with ...........3347

can anyone recheck my work please

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:

Originally Posted by http://www.doublemersennes.org/factors.php?id=anno

MM(31)

Factor : 295,257,526,626,031

for example.

[isaac]

thanks a lot!

back to the drawing board i guess :)

[CRGreathouse]

What caused you to say that it was prime?

[TimSorbet]

Originally Posted by isaac

2^2147483647-1 is prime

its a every large number that ends with ...........3347

Actually, it ends with 3327.

[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?

[henryzz]

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...

[TimSorbet]

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!