Million digit moonshot

MooMoo2 · 2017-12-21, 17:01

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=1-3339989031 (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*2^3394939-1 is prime. To avoid duplicating work, the k's I tested are below.

Code:

Range    Status  Primes found Twins found
1-250000   Complete 0  0
339,999,765-343,320,885  Complete 1  0
456,902,325-460,289,391  Complete 0  0
646,837,449-650,329,911  Complete 0  0
764,416,521-768,017,871  Complete 0  0
953,970,549-957,450,741  Complete 0  0
1,071,363,081-1,074,911,595 Complete 0  0
1,260,952,149-1,264,213,299 Complete 0  0
1,377,924,459-1,381,383,759 Complete 0  0

The sieve file has a bit under 1.09 million candidates and is at: https://www.sendspace.com/file/xhhpab
The credit is all yours if you find a non-twin 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 1-10T (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

Puzzle-Peter · 2017-12-21, 17:45

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!

MooMoo2 · 2017-12-22, 05:41

Quote:

Originally Posted by Puzzle-Peter

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!

Thanks! I won't be doing any more ranges on this n in the near future, but there might be some people out there who're interested. As of today, primes of this length will be one of the 250 largest known primes. There's even a Wikipedia article about them:
https://en.wikipedia.org/wiki/Megaprime

Batalov · 2017-12-22, 05:57

Quote:

Originally Posted by MooMoo2

... the odds that any k/n pair in that file is twin is less than 1 in 1200.

Definitely and substantially less. How did you come up with such an estimate - 1 in 1200?

VBCurtis · 2017-12-22, 06:03

Quote:

Originally Posted by Batalov

Definitely and substantially less. How did you come up with such an estimate - 1 in 1200?

Pretty sure he took his estimate that a twin would happen every 4T k's, and divided by the k-range 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.

Batalov · 2017-12-23, 00:59

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?

MooMoo2 · 2017-12-23, 01:08

Quote:

Originally Posted by Batalov

Definitely and substantially less. How did you come up with such an estimate - 1 in 1200?

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.

science_man_88 · 2017-12-23, 01:47

Quote:

Originally Posted by MooMoo2

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.

Depends on how you measure probability. The odds should be ((1.37G-1)^1.08M)/(1.37G^1.08M) if independent, for them all not being twin.

Batalov · 2017-12-23, 02:32

Quote:

Originally Posted by MooMoo2

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.

Ah. You want someone to take your whole file and have a 1 in 1200 chance to find a twin, that's ok. That's about right. But that's not what can even remotely happen, is it?

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 (6-year old) computer.

MooMoo2 · 2017-12-23, 17:36

Quote:

Originally Posted by Batalov

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.

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.

2017-12-21, 17:01	#1
MooMoo2 Aug 2010 2·3·103 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=1-3339989031 (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 *3429246512^3394939-1** is prime. To avoid duplicating work, the k's I tested are below. Code: Range Status Primes found Twins found 1-250000 Complete 0 0 339,999,765-343,320,885 Complete 1 0 456,902,325-460,289,391 Complete 0 0 646,837,449-650,329,911 Complete 0 0 764,416,521-768,017,871 Complete 0 0 953,970,549-957,450,741 Complete 0 0 1,071,363,081-1,074,911,595 Complete 0 0 1,260,952,149-1,264,213,299 Complete 0 0 1,377,924,459-1,381,383,759 Complete 0 0 The sieve file has a bit under 1.09 million candidates and is at: https://www.sendspace.com/file/xhhpab The credit is all yours if you find a non-twin 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 1-10T (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 2017-12-21 at 17:16

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2017-12-21, 17:45	#2
Puzzle-Peter Jun 2009 683 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!

2017-12-23, 00:59	#6
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,391 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?