20171221, 17:01  #1 
Aug 2010
2^{2}·3·47 Posts 
Million digit moonshot
I was looking for my first million digit prime, and I figured that I might as well search for twins at the same time. So I picked an n, chose a range of k=13339989031 (3.34 G), and sieved it to p=3300T for twins. The candidates take approximately 2 hours to test on one core, and using all four cores on a quad core would boost your production rate to one test every half an hour. On average, you can expect to find one prime every ~37,000 tests, so using two quad cores on this would yield an average of one prime a year.
I randomly picked some ranges, got lucky, and only needed to test ~9,000 k/n pairs before finding that 342924651*2^33949391 is prime. To avoid duplicating work, the k's I tested are below. Code:
Range Status Primes found Twins found 1250000 Complete 0 0 339,999,765343,320,885 Complete 1 0 456,902,325460,289,391 Complete 0 0 646,837,449650,329,911 Complete 0 0 764,416,521768,017,871 Complete 0 0 953,970,549957,450,741 Complete 0 0 1,071,363,0811,074,911,595 Complete 0 0 1,260,952,1491,264,213,299 Complete 0 0 1,377,924,4591,381,383,759 Complete 0 0 The credit is all yours if you find a nontwin prime with that sieve file, but we'll share the credit if you do find a twin. It's not likely, though  the odds that any k/n pair in that file is twin is less than 1 in 1200. To have a ~90% chance of finding a twin, you'll need to sieve from 110T (or 10,000 n's to 1G), which will yield a twin every 4T on average. But you can't find a million digit prime or twin if you don't give it a shot. So download the file, try your luck, and use this thread to coordinate your ranges searched Last fiddled with by MooMoo2 on 20171221 at 17:16 
20171221, 17:45  #2 
Jun 2009
2·5·67 Posts 
Haha, this is great. Sometimes I fool around with stuff like that myself, just for entertainment. And hey  who knows, right? I tried million digits twins and 100K digits triplets just for fun. So far, no luck just as I expected. But it's fun and that's the importand thing in my book.
So I won't join in but I wish you good luck and lots of fun with your project! 
20171222, 05:41  #3  
Aug 2010
1064_{8} Posts 
Quote:
https://en.wikipedia.org/wiki/Megaprime 

20171222, 05:57  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×2,281 Posts 

20171222, 06:03  #5 
"Curtis"
Feb 2005
Riverside, CA
2^{2}×3×359 Posts 
Pretty sure he took his estimate that a twin would happen every 4T k's, and divided by the krange in his file. He sieved 1/1200th of the range that would have one expected twin, so said the file is 1/1200th chance to have a twin.

20171223, 00:59  #6 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,281 Posts 
Why 4T? This 4T thingy is a red herring.
Let me ask in a different way. If he says that the probability of finding a prime is estimated at 1:37000 (which is in the correct ballpark), then why is the probability of it being part of the twin not exactly the same 1:37000, huh? 
20171223, 01:08  #7 
Aug 2010
1000110100_{2} Posts 
Each candidate has a 1 in ~1.37G chance of being twin (~37000^2). Since there are ~1.08 M k/n pairs in the sieve file that haven't been tested yet, the chance that any one of them is twin is approximately 1 in (1.37G/1.08M) = 1 in ~1269.

20171223, 01:47  #8 
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} Posts 
Depends on how you measure probability. The odds should be ((1.37G1)^1.08M)/(1.37G^1.08M) if independent, for them all not being twin.

20171223, 02:32  #9  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×2,281 Posts 
Quote:
People will take a minuscule fraction of the file and think "if I find a prime, it has a 1:1200 chance to be a twin! I like these odds!" That's what is going to happen. P.S. If you wanted someone to do the whole file, then it is way undersieved. I can remove 1000 candidates from it in a day  while I cannot PFGW/LLR 1000 in a day on the same (6year old) computer. 

20171223, 17:36  #10 
Aug 2010
564_{10} Posts 
No, if you find a prime on that file, it has about a 1:37000 chance of being a twin. Apologies if anyone was confused or misled by my initial post.

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