Twin primes in the 50,000 digit range?

[wblipp]

Originally Posted by thommy

When i get a prime every 500 candidates i test, i think i ll possible have to find 500 primes (so checking 500*500=250000) candidates to find a twin prime.

That estimate implicitly assumes that primality x and x+2 are independent events, but they aren't. For example, x not divisible by 3 makes the probability x+2 is not divisible by 3 only 1/2 instead of 2/3. The sum of all of these is effects is known as the twin prime constant, and it's value is about 0.66. In consequence, you should expect to check 500 * 500 * (1/0.66) candidates, about 50% more than your estimate.

You may also need some luck from Poisson. While the average number of twin prime pairs should be 1, that includes combinations of zero, one, two, three and more twin primes. The probability of "n" twins should be Poisson distributed, which means that if the expected number is "n", the probability of zero twins is exp(-n). This is a disappointingly large 37% at the point the expected number is 1.

Good luck with the search.

[jasong]

Is the original poster of this thread still around? Trying to set a new twin prime record with a distributed attack sounds like a fun project.

[Joshua2]

Yes, I am, still going at it sieving. Sieved up to 214 trillion. Still getting them one every 3 seconds. On a 3.4 ghz P4 it takes 60 seconds to do an llr. On an 2600+ AthlonXP it takes about 120 seconds. On an old P3 600 mhz it takes about 620 seconds to do one. So it seems I will be sieving for a long time. However, there are just over 12 million candidates left, and I will never be able to test that many, unless we can get a distributed team going. If we are only going to test say half of them, then I will only need to sieve half as high.
With 12 million left at 3 seconds (AthlonXP and P4 seem to be around the same speed) each, it will take at least 10,000 hours (A little over one 2600+ AthlonXP or 3.4 Ghz P4 year). It will approach 200,000 hours (or almost 23 3.4 ghz P4 years) if we had to llr them all. (assuming my calculations are correct)

[smh]

On a 3.4 ghz P4 it takes 60 seconds to do an llr.

It's been a long time since i did prp tests, but 60 seconds a test......

[Joshua2]

I've made a couple edits to my post just above, bad caluclations it seemed. I think they are right now though. I also added in more times.
SMH, 60 seconds? long, short, normal?? I'm guessing long...