Re: [PrimeNumbers] Re: Twin Record
> Wow!Daniel Papp used the 'classical' method for his discovery
> On merely the 6th Proth-find, it seems:
> unless Daniel Papp has a huge backlog of g259
> Proth-finds to post.
> But then, think of all those Proth cycles
> looking for plain top5000 cannon fodder.
The expected number of twins in 3-33,218,925 for n=169690 is
Sum [k odd = 3 to 33218925] 1.32 * (2 / log(k*2^169690))^2 = 0.006.
The first twin was expected for k=5,000,000,000 !
But if 200 people are searching for a twin prime record around n=169690,
then 33,218,925 was the expected k.
- Thanks for the twin heuristics, Yves.
Apologies to Daniel; his bio indeed recounts
that he was smart as well as very lucky.
Given his NewPGen sieve, it would need
David Underbakke to say just how lucky.
Meanwhile the triplet record crept up.
First I found a 7-11-13 BLS triplet a shade low:
and then another just a shade bigger
than the day-old 5-7-11 record:
The heuristics of this
twin-seed ==> quintuple sieve ==> 3 goes at a triplet
method are hairy to compute, but I think
I was lucky by a factor of about 2.
My Poissonian guess was a mean somewhere between
1 and 2 hits and I got 4.
But maybe I screwed up the heuristics;
it entailed a fiendish 5-fold filter, hand crafted
in base 35 and written in ForTran (of course).
Anyway, I ain't complaining about the 4 hits instead of 2 :-)
- I would also like to add my congratulations to Daniel on his new twin prime
record. I hope the discovery leaves him smiling for a very long time.
My comments on luck below should not detract from the fact that Daniel chose
an intelligent course of action and achieved his goal. It is the discovery
that is the goal and reward, not the number of attempts along the way.
There is a certain amount of luck in any twin prime/Sophie Germain discovery.
I was just as happy finding 318032361.2^107001+/-1 with only 60 primes found
(very lucky) as I was finding 1807318575.2^98305+/-1 after finding nearly
1000 primes (expected primes). (Both efforts with Phil Carmody)
Daniel, be very very happy with your discovery. You have achieved an
important goal that will be in the top twenty pages for a very long time.
Yves Gallot wrote:
>The expected number of twins in 3-33,218,925 for n=169690 isI would elaborate on this. If 200 people are searching, then 1 of those 200
>Sum [k odd = 3 to 33218925] 1.32 * (2 / log(k*2^169690))^2 = 0.006.
>The first twin was expected for k=5,000,000,000 !
>But if 200 people are searching for a twin prime record around n=169690,
>then 33,218,925 was the expected k.
people would find a twin by searching a range of 33,218,925 assuming that
each one was searching a different n value. That is still a 0.5% chance
that a specific individual would find it in that range.
David Broadhurst wrote:
>Thanks for the twin heuristics, Yves.All the discussions already include the assumption that a good sieve was
>Apologies to Daniel; his bio indeed recounts
>that he was smart as well as very lucky.
>Given his NewPGen sieve, it would need
>David Underbakke to say just how lucky.
applied before PRP testing. To find a twin prime larger than Daniel's
record, I will have to use 10 Ghz of processing for 3-4 years to have a
better than even chance.
Anyone who is willing to make that commitment should get full credit for the
discovery no matter when it happens. I give Daniel full credit for his
discovery, as indicated at the start of this message.