20150703, 18:30  #1 
Aug 2010
2·293 Posts 
Top 3 twin found!
4884940623*2^1988001 is prime! (59855 decimal digits) Time : 14.689 sec.
4884940623*2^198800+1 is prime! (59855 decimal digits) Time : 14.608 sec. https://primes.utm.edu/primes/page.php?id=120068 https://primes.utm.edu/primes/page.php?id=120069 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, 020M: unknown Sieve depth, 20M4916M: 3200T Candidates per 1M: 306 (from 20M4916M) Total Primes found: 765 (includes the +1 twin) Total Candiates tested: approximately 1609500 Candidates tested, 020M: approximately 9500 Candidates tested, 20M4916M: 1,600,004 Riesel prime density: 1 every 6.43M. Candidates per riesel prime: 2100 (from 204916M) 2107 (from 04916M) 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. 
20150703, 19:30  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×3^{3}×13^{2} Posts 
Congrats! (from someone who knows how hard it is. It is, indeed!)

20150703, 19:37  #3 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10001110100110_{2} Posts 
Have you kept all intermediates? I have an offer for you that you can't refuse!
I have run on and off a certain search for which I need many approximately this 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 the Hungarians (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 halfprimes. 
20150703, 22:11  #4  
Aug 2010
586_{10} Posts 
Quote:
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. 

20150713, 23:30  #5 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10001110100110_{2} Posts 
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*2^1988001)*(299771367*2^1988001)) is composite: RES64: [DB6C0836F42F050D] Phi(5,(125526867*2^1988001)*(299771367*2^1988001)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 can 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. These are more interesting and rare. They are provable by N1 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 one of these but it was not eligible for Top5000. Just a little too small. 
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