10th Prime!!

[Alien88]

19249 * 2^13018586 + 1 is prime! We've done it again and are now down to 7 primes.

I think this is the first prime we've verified without our users noticing! Congrats to Konstantin Agafonov and his team, TSC! Russia, who discovered this prime. The official press release is at http://www.seventeenorbust.com/docum...s-050507.mhtml

[Bok]

That was out of the blue!

Congrats guys!

Bok

[Gruznov]

I'm so happy!!!

[engracio]

Wooohoo


e

[vjs]

And one of the lighter weight ones too!!!

Very cool!

[axn]

It is the fifth largest-known prime overall and the tenth such
discovery for the project in its five year history.

The new one comes in at 7th overall, not 5th overall as the press release says.

Oh, and

[jjjjL]

The new one comes in at 7th overall, not 5th overall as the press release says.

Good catch. Thanks!

Fixed.

[hhh]

I updated the wikipedia page; it still lacks the exact digit count. Can somebody please? H.

[Sceptic]

Ahh... Great news to start the day
Congratulations to Agafonov and his team TSC! Russia

Sceptic

[axn]

I updated the wikipedia page; it still lacks the exact digit count. Can somebody please? H.

Done.

[Matt]

NIce work guys!

[gopher_yarrowzoo]

Congrats always nice when one is found by one of the smaller teams....
Oh well 10 down, 7 to go..

[hhh]

I did the french wikipedia as well. Still remaining are the italian, the duch and the chinese one. But I don't feel concerned here. H.

[philmoore]

Congratulations! Very nice find!

This discovery brings Payam Samidoost's "mixed Sierpinski problem" within easy resolution. For those who don't know, the extension of the Sierpinski problem from numbers of the form k*2^n + 1 with positive integers for the exponent to those with negative integers for n leads to the consideration of the numbers k + 2^n for postive n. A finite covering set for one case is necessarily a covering set for the other case, and the "dual Sierpinski problem" is to find prime values of k + 2^n for every odd value of k less than 78557. The "mixed Sierpinski problem" is, for each such value of k, to either find a prime value of k*2^n + 1 or of k + 2^n. This mixed problem is weaker than the original problem posed by Selfridge, but the truth of the mixed problem certainly lends a strong indication of likelihood of the original conjecture. The last three values of k to be eliminated from the mixed problem are 19249, 28433, and 67607, and now these first two values have been eliminated by the Seventeen or Bust project. Actually, PROBABLE primes of the form k + 2^n were discovered in 2002 by Payam Samidoost, 19249 + 2^551542, and Jim Fougeron, 67607 + 2^16389, but there was not much prospect for proving this first number actually prime. However, the second number, 67607 + 2^16389 with only 4934 decimal digits, should be easily provable using Elliptic Curve Primality Proving, and will complete the resolution of the mixed problem.

I see that the latest version of Marcel Martin's Primo (3.0.2) is limited to numbers not exceeding 10000 bits, about 3000 digits, but if someone has a recent but previous version (one of the versions 2.x.x), I would guess that a primality proof of 67607 + 2^16389 would take a month or two on a fast CPU. Is anyone game?

[tqft]

If someone has the program I am game.

needs to run on Ubuntu Dapper - fully patched - any special libraries required?

Am not afraid to compile it if necessary.

[philmoore]

I don't know anything about Ubuntu. The version of Primo I used several years ago was an executable which ran under Windows. For awhile, the author Martin wouldn't authorize its use in Britain and the U.S. due to software patent issues, so I am hoping someone else may have an older version.

[jjjjL]

I recall this problem. I believe it's referred to as the Dual Sierpinski Problem. It is documented at http://sierpinski.insider.com/dual

I'm really excited about the prospect of settling it completely! As you said, creating the primality certificate with PRIMO for that size number should be feasible using a modern computer (given a month or so). Someone track down that binary... then someone with a fast computer start creating the certificate... send me an email with an ETA... then send me the certificate and I'll post the news for people that the Dual Sierpinski Problem is officially settled.


_
Louie

[Samidoost]

Great JoB!
Congratulations to SoB!
Payam

[philmoore]

I got ahold of a copy of Primo 2.3.2 which should be able to do this number. I am checking first with Jim Fougeron to make sure that it hasn't already been certified prime, but if he says it hasn't, I plan to go ahead with it.

By the way, the smallest dual Sierpinski primes for the other 6 exponents are all quite modest in size:
10223 + 2^19
21181 + 2^28
22699 + 2^26
24737 + 2^17
33661 + 2^72
55459 + 2^14
67607 + 2^16389

[riptide]

I recall this problem. I believe it's referred to as the Dual Sierpinski Problem. It is documented at http://sierpinski.insider.com/dual

I'm really excited about the prospect of settling it completely! As you said, creating the primality certificate with PRIMO for that size number should be feasible using a modern computer (given a month or so). Someone track down that binary... then someone with a fast computer start creating the certificate... send me an email with an ETA... then send me the certificate and I'll post the news for people that the Dual Sierpinski Problem is officially settled.


_
Louie

Well I got a QX6700 at 3.3-3.4Ghz atm running SOB. I'd be game to put that dual problem to bed. Can the program be split to run 4 executables looking at diff areas of the numbers.? I doubt its multi threaded.

Also have a E6600 at 3.8Ghz.?

[philmoore]

The Sierpinski conjecture: "78557 is the smallest odd k such that k*2^n+1 is composite for all positive integers n." (Sometimes called the Selfridge conjecture, as Sierpinski only posed the problem of finding the smallest such k.)

The dual Sierpinski conjecture: "78557 is the smallest odd k such that k+2^n is composite for all positive integers n."

The "mixed" Sierpinski conjecture: "78557 is the smallest odd k such that both k*2^n+1 and k+2^n are composite for all positive integers n."

The mixed conjecture is the one which the recent SoB discovery has put very close to resolution right now. I am posting updates on another thread. The dual conjecture has a ways to go, I don't think much progress has been made on it since 2002. See: http://sierpinski.insider.com/dual . There were only eight k values left at the time that Seventeen or Bust started with 17 values, so the dual conjecture may in fact be easier to solve, but the large primes discovered in the dual search are only probable primes, so it won't be settled as rigorously as for the original Sierpinski problem.