Largest known prime
 

When was the last time that the largest known prime number was not a Mersenne prime?

1989, according to [url]http://primes.utm.edu/notes/by_year.html#table2[/url]

391581*2^216193-1 was found to be prime by the Amdahl Six while Slowinski's Cray search was working its way from M216091 to M756839.

largest
 

im using a factoring programme that i just downloaded and decided to try factoring the largest known prime,2^43112609-1, and it says that it has factors,what could i be doing wrong or what could be wrong with the programme?

[QUOTE=Unregistered;152628]im using a factoring programme that i just downloaded and decided to try factoring the largest known prime,2^43112609-1, and it says that it has factors,what could i be doing wrong or what could be wrong with the programme?[/QUOTE]What program are you using? How did you enter the number? Many factoring programs only want the exponent given to it. If the way you entered the number caused the program to think that you wanted to factor 2^(43112609-1), of course there is a factor for that.

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.

[QUOTE=Unregistered;152628]im using a factoring programme that i just downloaded and decided to try factoring the largest known prime,2^43112609-1, and it says that it has factors,what could i be doing wrong or what could be wrong with the programme?[/QUOTE]

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 2^43112609-1. (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.)

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.

[quote=Unregistered;152754]Please enter the [B]exponent[/B] to be factored: [B]2^[/B]43112609[/quote]
There's the problem. It was asking for the exponent, and you told it 2^43112609, not 43112609. 2^2^43112609-1 is indeed composite, since its exponent is composite (specifically, its exponent is divisible by 2, so 2^2-1=3 divides 2^2^43112609-1).
[URL]http://en.wikipedia.org/wiki/Mersenne_prime#Searching_for_Mersenne_primes[/URL]

[QUOTE=Unregistered;152754]i think its factor 3 or something like that,

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?[/QUOTE]If the program is Luigi's Factor4 (or 5), you need to only input the exponent.

The fact that you are to 2^100 tells me that, you are likely to [B]not[/B] be factoring the number that you [B]think[/B] that you are. It would take a [COLOR="Red"][B][SIZE="4"][FONT="Arial Black"]tremendously long time[/SIZE][/FONT][/B][/COLOR] 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.

[QUOTE=Uncwilly;152853]If the program is Luigi's Factor4 (or 5), you need to only input the exponent.

The fact that you are to 2^100 tells me that, you are likely to [B]not[/B] be factoring the number that you [B]think[/B] that you are. It would take a [COLOR="Red"][B][SIZE="4"][FONT="Arial Black"]tremendously long time[/SIZE][/FONT][/B][/COLOR] 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.[/QUOTE]

Confirmed. It seems my program without the initial wekcome banner... :smile:
Mind that it is slower than Prime95 (unless you run 8 concurrent threads, of course).
The number he is checking is definitely prime.

Luigi

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.

[quote=Unregistered;152881]ive realised that (2^43112609)-1 doesnt have a factor.[/quote]

It has two factors: 1 and 2^43112609-1. I think you meant proper factors.

Sorry about this one, I thought I just [I]had [/I]to put it in.