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-   -   Top 3 twin found! (https://www.mersenneforum.org/showthread.php?t=20340)

MooMoo2 2015-07-03 18:30

Top 3 twin found!
 
4884940623*2^198800-1 is prime! (59855 decimal digits) Time : 14.689 sec.
4884940623*2^198800+1 is prime! (59855 decimal digits) Time : 14.608 sec.

[url]https://primes.utm.edu/primes/page.php?id=120068[/url]
[url]https://primes.utm.edu/primes/page.php?id=120069[/url]

It's the 3rd largest of all time and the largest found by an individual who's unaffiliated with any project. It also beats the original n=195000 TPS record and would have been the largest known twin if it were found before August 2009.

Stats:
[code]
Sieve start date: January 26, 2015
Sieve end date: April 8, 2015
Discovery date: June 30, 2015 11:45 PM
Computer used in discovery: Intel Core i7 4790
Verification date: July 1, 2015 10:57 PM
Computer used in verification: AMD Phenom II X6 1055T
Number of cores used: 10
Total GHz: 31.2
Sieve depth, 0-20M: unknown
Sieve depth, 20M-4916M: 3200T
Candidates per 1M: 306 (from 20M-4916M)
Total Primes found: 765 (includes the +1 twin)
Total Candiates tested: approximately 1609500
Candidates tested, 0-20M: approximately 9500
Candidates tested, 20M-4916M: 1,600,004
Riesel prime density: 1 every 6.43M.
Candidates per riesel prime: 2100 (from 20-4916M)
2107 (from 0-4916M)
[/code]

I was a bit lucky - the probability that a twin would be discovered after searching 4.9 G is only 29%. This is also the lowest k that produces a twin for this n.

But I wasn't that lucky. Finding it involved testing about 50% more candidates and sieving almost three times deeper than TPS's n=195000 project. Despite this, it took me less time to find the n=198800 twin than it took for TPS to find the n=195000 twin.

For those of you who're interested, the first few numbers of the decimal expansion of 4,884,940,623*2^198800+1 are 28,313,743,191,542,... ,and the last few numbers are ...2,658,872,885,249.

Batalov 2015-07-03 19:30

Congrats! (from someone who knows how hard it is. It is, indeed!)
:banana::banana::banana:

Batalov 2015-07-03 19:37

Have you kept all intermediates? I have an offer for you that you can't refuse! :lol:
I have run on and off a certain search for which I need many approximately[I] this[/I] sized primes. You will have 0.5 of a prime if it works, of course. PM me if interested.
I have in the past similarly contacted[I] the Hungarians[/I] (as DavidB called them, see positions #6,7,8) and other twin searchers, as well as I've processed all of my position #5 interim half-primes.

MooMoo2 2015-07-03 22:11

[QUOTE=Batalov;405249]Have you kept all intermediates? I have an offer for you that you can't refuse! :lol:
I have run on and off a certain search for which I need many approximately[I] this[/I] sized primes. You will have 0.5 of a prime if it works, of course. PM me if interested.
I have in the past similarly contacted[I] the Hungarians[/I] (as DavidB called them, see positions #6,7,8) and other twin searchers, as well as I've processed all of my position #5 interim half-primes.[/QUOTE]
Offer accepted :smile:

If anyone's interested in my lresults files and/or the raw sieve file (k=20M - 60020M, n=198800, p=3200T, about 18 million untested k/n pairs), PM me, and I'll send you the link if you'll agree to share credit for any notable primes found.

Batalov 2015-07-13 23:30

Unfortunately, no derivative primes were found.

Here are the examples of the tested candidates to give you a flavor of what was done:
[CODE]Phi(10,(46421883*2^198800-1)*(299771367*2^198800-1)) is composite: RES64: [DB6C0836F42F050D]
Phi(5,(125526867*2^198800-1)*(299771367*2^198800-1)-1) is composite: RES64: [81248E7866F4AD15]
and a few thousand more...
There are a 200K of similar canidates easily produced and some of them are likely prime and [B]can[/B] be found
but the cost of sieving and testing is too high to go on for too long.
Besides I already have a couple of primes like these.
[/CODE]
What was of primary interest, though, and what I 100% searched were all Phi(5,p), Phi(7,p), Phi(10,p+1), Phi(14,p+1) for all of your several hundred p.
These are more interesting and rare.
They are provable by N-1 because p and p+1 are fully factored which makes
Phi(5,...)-1 and Phi(10,...)-1 50% factored and Phi(7,...)-1 and Phi(14,...)-1 33.333% factored which is enough got the proof.
Other polynomials can be tried (and tried and tried until a constructible prime is found) but they are not as interesting as Phi().
I have [URL="http://www.mersenneforum.org/showpost.php?p=397246&postcount=50"]one of these[/URL] but it was not eligible for Top5000. Just a little too small.


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