20081104, 22:22  #1 
4,751 Posts 
Largest known prime
When was the last time that the largest known prime number was not a Mersenne prime?

20081104, 22:44  #2 
(loop (#_fork))
Feb 2006
Cambridge, England
1100100110110_{2} Posts 
1989, according to http://primes.utm.edu/notes/by_year.html#table2
391581*2^2161931 was found to be prime by the Amdahl Six while Slowinski's Cray search was working its way from M216091 to M756839. 
20081209, 18:04  #3 
2·43·89 Posts 
largest
im using a factoring programme that i just downloaded and decided to try factoring the largest known prime,2^431126091, and it says that it has factors,what could i be doing wrong or what could be wrong with the programme?

20081210, 14:16  #4  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
47·233 Posts 
Quote:
The LL is a conclusive test. There were enough different runs on different hardware with different code to prove there was no error in the testing. 

20081210, 17:18  #5 
Aug 2006
2^{2}×3×499 Posts 
Does it tell you the factors? The numbers involved are small enough (5 MB) that you could just take the gcd with a program like Pari to prove to yourself that the 'factors' don't actually divide 2^431126091. (Pari takes ~20 seconds on my machine to do the gcd, or less if the factor is significantly smaller than the square root of the number.)
Last fiddled with by CRGreathouse on 20081210 at 17:20 
20081210, 18:54  #6 
3944_{10} Posts 
A
i think its factor 3 or something like that,i think ive figured it out,it seems to close down when it finds a factor.this is an example of what happens.
Please enter the exponent to be factored: 2^43112609 Now enter start bit depth : 1 Finally enter end bit depth : 70 Sieving from 2^2 up to 2^70... k=13853571, d=1194527127847231 50.003 bit depth the "k=13853571, d=1194527127847231 50.003 bit depth" is the part that confused me,i thought this meant it had found a factor.im factoring a number at the minute,ive factored it up until,2^100 and it still hasnt found a factor,should i try factor it further or maybe try another method,if so what? thanks for all your help. 
20081210, 21:26  #7 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11×389 Posts 
There's the problem. It was asking for the exponent, and you told it 2^43112609, not 43112609. 2^2^431126091 is indeed composite, since its exponent is composite (specifically, its exponent is divisible by 2, so 2^21=3 divides 2^2^431126091).
http://en.wikipedia.org/wiki/Mersenn...ersenne_primes Last fiddled with by TimSorbet on 20081210 at 21:27 
20081211, 07:37  #8  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
47×233 Posts 
Quote:
The fact that you are to 2^100 tells me that, you are likely to not be factoring the number that you think that you are. It would take a tremendously long time to get to that level. (Decades ?) No, don't try that number anymore. Once it has passed 4 different LL tests on 4 different computers, using at least 3 different programs, IT IS PRIME. Last fiddled with by Uncwilly on 20081211 at 07:38 

20081211, 10:48  #9  
Banned
"Luigi"
Aug 2002
Team Italia
43×113 Posts 
Quote:
Mind that it is slower than Prime95 (unless you run 8 concurrent threads, of course). The number he is checking is definitely prime. Luigi 

20081211, 11:17  #10 
9,157 Posts 
sorry i should of highlighted what what part i entered, when you open the program it comes up 2^ and all you do is enter the exponent.ive realised that (2^43112609)1 doesnt have a factor.however my new number doesnt have one up as far as 2^60,what test should i carry out on it now or should i try and factor it a bit more?
Thanks. 
20081211, 12:50  #11 
Nov 2008
2×3^{3}×43 Posts 
It has two factors: 1 and 2^431126091. I think you meant proper factors.
Sorry about this one, I thought I just had to put it in. Last fiddled with by 10metreh on 20081211 at 12:52 
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