text:
One of the small compensations for journalists attending investment conferences, where panel discussions can at times degenerate into speakers starting to sound a little too alike, is the ability to meet with executives in a side lounge and maybe get a fresher perspective.
It's not that Martha King, the head of Vanguard's advisory business, dropped any news bombs during our sidehall meeting at IndexUniverse's Inside ETFs conference. King is too smart to be induced to say something that should be protected from industry competitors. (She politely bypassed my question about the financial terms of Vanguard's new licensing agreements with the CRSP and FTSE indexes.)
But there's less guardedness in a face-to-face meeting and that just makes it easier to cut through the formulaic responses one comes to expect from the various sages on stages.
About those new indexes, for example. Vanguard shook up the indexing universe in October when it announced it was ending its relationship with MSCI as the provider of indexes for 22 of its ETFs, switching instead to University of Chicago-affiliated CRISP and the Financial Times' FTSE indexes.
While trumpeting the firm's smooth execution of the transition, she frankly acknowledged there were some clients who complained and wanted to move on to what they regarded as greener pastures. She said the firm anticipated this from the outset as a consequence of a business changing vendors.
The move was planned long in advance. "Vanguard doesn't do anything precipitously," King said.
While Vanguard made it clear the move was aimed at maintaining the firm's vaunted low-cost value proposition into the future, King was—once again—quite open about the unpretty sausage-making process in the ETF world:
"There has been a shift in power toward benchmark providers and they have been increasing the fees that they charge, particularly in a market where discernible differences are harder and harder to find," the Vanguard executive said. "Usually where that happens in an industry, prices come down. But that has not been happening here."
With the change in index vendors, "we now have cost certainly," King said. (It was here that she declined my question on how much those costs were and for how long they could be expected to remain.)
On another cost-related issue—that of rival Charles Schwab Corp.'s newly launched commission-free trading platform—King was dismissive of the value being offered.
"Whether you're talking mutual funds or ETFs, nothing's free, somebody's paying.
"Take a look at what products are on that platform; it's not best of breed." She asked whether an investor wanted something free or would rather have a "best-in-class product and pay a small cost to trade it."
A final example of King's unexpected candor concerned Vanguard's relationship with advisors.
Remember, King is "head of U.S. financial intermediaries" for the fund group, yet the Vanguard exec said that advisor product petitions is actually last on the list of considerations in the firm's new product decisions.
"Vanguard has a set of product development principles," King said.
Before the firm seeks advisor input, a product idea "has to have an enduring place in the portfolio. Second, we have to have a benchmark that can invest in it in a high-quality way. Then we have to be able to bring it to market and be highly competitive."
Listening to advisors, though, is part of the very structure of Vanguard's outreach efforts, staring with the firm's decision to have its "field sales people"—what other firms term "wholesalers"—living in the communities they serve.
"Advisors see that as 'you are really committed to us,'" King says.
The rest is the classic "consultative selling" approach, she adds.
"The fastest way to not be a salesman at Vanguard anymore is to put a client in a product they don't need."
It's all about listening to the advisor, she says. "We have no sales quotas; [the wholesaler] is going to be understanding what the advisor's trying to do," she adds.
As for the end user, King stands fast by the firm's ultimate value proposition, and in that sense her comments were entirely predictable:
"Costs have always mattered," she says. "Cost is only going to matter more and more. So it's really the job of the advisor to sort through the myriad products out there. It's a noisy marketplace."


text:
|Mail Online
In 2009 Prince William was made a honorary barrister at Middle Temple. At the time William was a trainee RAF helicopter pilot and during his speech in the Inn's Elizabethan Hall in front of almost 300 guests he 'promised not to practice, except for the odd speeding ticket' (you can read William's full speech here). Other members of the Royal family called to the bench include the Queen, called in 1944 and Diana, Princess of Wales, called in 1988.
Middle Temple is one of the four Inns of Court entitled to call their members to the English Bar as Barristers. It is located in the wider Temple area of London near the Royal Courts of Justice.
|Middle Temple
In the 13th century, the Inns of Court originated as hostels and schools for student lawyers. The Inns stopped being responsible for legal education in 1852, although they continue to provide training in areas such as advocacy and ethics for students, pupil barristers and newly-qualified barristers. Most of the Inn is occupied by barristers' offices. One can take a virtual tour of the picturesque Inn here.
|Middle Temple
Middle Temple Hall is at heart of the Inn and the Inn's student members are required to take qualifying sessions there. The Hall is also very popular for weddings, banqueting and receptions. It has also become a much used film location. Shakespeare's Twelfth Night received it's first recorded performance here.
|Middle Temple Hall
Kate looked chic in a burgundy suit by French ready to wear brand Paule Ka. The double breasted jacket and short skirt with horizontal ribbing looked sophisticated yet youthful and burgundy is very much on trend for Autumn/Winter.
Eagled eyed Anna from My Small Obsessions noted the suit is possibly the same outfit she wore to a pre-christmas lunch in December 2011.
|Roland Hoskins/Daily Mail
Paule Ka was created in 1988 by Serge Cajfinger and is now established in 54 countries and distributed throughout the world. The brand is described as
'Respecting glamour from a Hollywood movie screen. But always set against an iconic Parisian backdrop, Paule Ka's style breaks through conventional ideas and plays with contrasts, volume, symmetry, humour and seduction'.
A look at pieces from the Autumn/Winter collection.
|Paule Ka
The Duchess wore a lace top underneath and black tights.
Kate wore her Episode Angel pumps (with thanks to What Kate Wore)
Kate did not carry a clutch and accessorised with gold and black drop earrings.
You can watch a video from the visit at ITN Source and a selection of photographs from the visit at Just Jared.
Earlier today Clarence House announced William will not be joining Kate in Tyne and Wear and Stockton-on-Tees on Wednesday as he plans to attend the funeral of Olga Powell, who was his and Prince Harry's beloved nanny for much of their childhood. A spokesman said 'given the significant role that Mrs. Powell played in the Princes' lives. The Duke wished to pay his respects in person'. It will be Kate's busiest solo day's work since becoming a member of the Royal family with four engagements to attend.
|Clarence House Twitter
Tomorrow William and Kate will attend the opening of the FA's new National Football Centre, St George's Park.

subset: commoncrawl


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Washington Post contributor Jim Shahin had some choice words for Charlotte barbecue recently. Stopping in Charlotte-Douglas International Airport, he contemplated our city while getting a barbecue sandwich from Brookwood Farms Carolina Pit BBQ:
"I was in an airport, ordering faux Carolina 'cue, and I was lost. Technically, I suppose, I was in Charlotte. But the city is itself lost, barbecue-speaking. It does not adhere to one of the state's famously partisan styles, whether Eastern or Western.
"As a city within one of the great barbecue regions, Charlotte is regarded as a barbecue embarrassment. If Charlotte were a relative, it would be the one everyone wished didn't come to Thanksgiving."
Is that fair? Is Charlotte that much of an embarrassment? Does someone from Washington -- the flattest flavor spot between Baltimore and New York -- have any experience at knowing what tastes good?
Share your opinion here and we'll pass them on to Shahin. A few ground rules: Keep your response concise; don't use profanity; and keep the personal insults to a minimum. Although Shahin did call our city an embarrassment. So the personal insults have already started to fly.
Tuesday, November 27, 2012
Barbecue: Are those fighting words?
Washington Post contributor Jim Shahin had some choice words for Charlotte barbecue recently. Stopping in Charlotte-Douglas International Airport, he contemplated our city while getting a barbecue sandwich from Brookwood Farms Carolina Pit BBQ:
36 comments:
- lkmnews said...
Hmmm... Juding a city's cuisine based on what's found in an airport? Not very smart, in my view.
Meanwhile, as I sit here in Uptown Charlotte, I can picture several fine 'cue experiences within a short drive south or west.
Hmmm. Or north. Or east. ;-)
- November 27, 2012 at 5:22 PM
- James said...
To judge a city for its food by its airport restaurants, especially for barbecue, is so far off base. The writer (?) needs to make a tour of several places to eat before he goes off on Charlotte BBQ. You can go to a number of BBQ places in town to get a better representation and probably 100% better than airport food.
- November 27, 2012 at 5:25 PM
- Anonymous said...
Has Mr. Shahin ever eaten at Reagan Airport, in his own hometown? I would guess not, since it is not wise for one who lives in a glass house to start a rock fight.
- November 27, 2012 at 5:30 PM
- Anonymous said...
As a critic willing to post a review based solely on an airport restaurant, Mr. Shahin is an embarrassment.
- November 27, 2012 at 5:33 PM
- Anonymous said...
there is no reason to take a yankee's opinion about Q seriously.
- November 27, 2012 at 5:33 PM
- Unknown said...
Mac's Speed Shop (S Blvd), that is all, some of the best BBQ in the country. And Lexington is just an hour drive away for the best BBQ in the state (if not the region) IMO.
Judging what is arguably the best state in the nation for BBQ by airport food is pretty tactless. It's an airport.
And technically, CLT falls neither in the Eastern or Western NC category...it's in the middle of the state.
- November 27, 2012 at 5:36 PM
- BBQJunkie said...
Mr. Shahin doesn't know Charlotte BBQ. Maybe there isn't a huge selection of Great BBQ joints...but there are some...not to mention quite a few award winning MBN and KCBS competition teams that call this great city home. Come on out to Blues and BBQ next year before you make your judgements Mr. Shahin...you'll get to see what Charlotte BBQ is all about.
- November 27, 2012 at 5:38 PM
- Emily said...
Who cares about "famously partisan styles"? They're relics of the past, back before cars and, yes, airplanes. Cooking Southern is all about defying categories. Making these irrelevant distinctions is like trying to leash a cat.
- November 27, 2012 at 5:43 PM
- Jim Laseter said...
The Washington Post generally attracts first-rate writers who know their stuff. What's more, they are used to great food as evidenced by the avails in the Washington area. But Charlotte Douglas is no more an example of the culinary offerings in Charlotte than National or Dulles are in DC. My biggest disappointment, however, is that the Observer even wasted the space to print our northern friend's comments.
- November 27, 2012 at 5:45 PM
- agFinder said...
No one thinks airport food represents anything besides airport food, especially not people who go through a lot of airports. This guy wrote something he hoped someone would re-post and ding ding ding! He got one!
- November 27, 2012 at 6:00 PM
- Sheldon Cooper said...
Perhaps he could provide more evidence than a horrible fast food restaurant in an airport before proclaiming CLT BBQ awful. He lacked any professionalism when he failed to provide backing to his argument.
Based on his logic I presume that all sub sandwiches in Washington DC are of the same caliber as the Subway that sits in the regional US Air terminal in Dulles. Bazinga.
- November 27, 2012 at 6:03 PM
- David said...
Charlotte does have a vibrant food scene, in my opinion. However when it comes to NC BBQ, I would agree, Charlotte isn't the best place. Mac's is ok and I really enjoy Midwood Smokehouse, but they are not quite what I think of when you say NC BBQ. Bill Spoons place would be close. When I think NC BBQ, I think about Stameys (Greensboro), Bridges(Shelby), B's (Greenville), Allen and Son's (Chapel Hill), Short Sugars (Reidsville), etc..and if you have been to any of those places, you would know that even the "feel" in those NC BBQ institutions are different and its kinda hard to come by that in Charlotte. Just my two cents.
- November 27, 2012 at 6:06 PM
- Anonymous said...
The author is right. There is no good cue in Charlotte. Shameful! Lancaster's was decent, that place on South Blvd that closes shortly after noon is ok, Jim and Nicks and Midwood are really good but not "authentic" Carolina cue. Mac's just a place for wanna a be bikers to gather and drink beer. Their cue is wanna bd also!
- November 27, 2012 at 6:09 PM
- Anonymous said...
I read the article on the Post's website. He wasn't critical at all - in fact, he was sort-of impressed by the airport food. His attitude was that he was surprisingly impressed by airport food, and that it did remind him of NC BBQ, which is actually a compliment. He's right, Charlotte isn't known for its BBQ like the areas all around it.
- November 27, 2012 at 6:15 PM
- Anonymous said...
C'mon the guy's right even though he was off base judging the city based on airport food alone. Charlotte is missing the boat on this one. Making a name for itself in the que world might have a modest affect on increasing tourism. We have a lot of ground to make up though. Memphis and Kansas City are way ahead. One strategy might be to feature restaurants that outwardly tout themselves as Lexington style, Shelby, or Eastern.
I'm just sayin'.
- November 27, 2012 at 6:27 PM
- Wiley Coyote said...
The only really good BBQ in Mecklenburg County comes from individuals like myself who smoke their own.
I'll give Mac's a thumbs up but that's about as close as you'll get to good BBQ here.... In my opinion of course.
- November 27, 2012 at 6:53 PM
- Anonymous said...
How did Washington get between Baltimore and New York?
- November 27, 2012 at 6:59 PM
- Anonymous said...
So true. Charlotte BBQ is lackluster at best. Everybody knows you have to go down to Lexington to eat quality bbq.
- November 27, 2012 at 7:01 PM
- Anonymous said...
As a barbecue spot, Charlotte is about an hour east of Shelby (either Red Bridges or Alston Bridges, natch).
And Washington is not between Baltimore and New York!
--born and raised in Shelby, now living in DC
- November 27, 2012 at 8:04 PM
- Anonymous said...
To judge a city's BBQ by sampling a corporate, homogenized airport location lacks insight and is just plain lazy.
- November 27, 2012 at 8:29 PM
- Anonymous said...
I agree with him. The BBQ at the airport is not good. BUT, there is plenty of good BBQ in and around the city. Next time, leave the airport and see the city.
- November 27, 2012 at 8:31 PM
- Anonymous said...
- This comment has been removed by the author.
- November 27, 2012 at 8:37 PM
- Anonymous said...
Somebody please give the author a map.
I suppose DC is between Baltimore and NY if you take a 28,000 mile route by driving South out of Baltimore first.
- November 27, 2012 at 9:11 PM
- Wiley Coyote said...
Also...Brookwood farms is out of Siler City.
- November 27, 2012 at 9:19 PM
- Anonymous said...
Airport fare is not the place to judge any community's food qualifications, and the BBQ at Douglas is not great, but better than the BBQ options in the Memphis and Dallas airports by far. Best airport food I have had is the southern at Paschal's in Atlanta Hartsfield. Mmmm, mm!
- November 27, 2012 at 9:20 PM
- Julie @ Willow Bird Baking said...
Sounds like someone's trying really hard to be the next Pete Wells. If you want to judge Charlotte's barbecue, come and eat at our barbecue restaurants -- not at our airport. A visit to Midwood Smokehouse for some brisket is in order!
- November 27, 2012 at 9:34 PM
- Anonymous said...
i suppose growing in lexington ruined me, but i have to say the yankee is right on. bill spoons is about as close as it gets to good, still too eastern for my taste - superb hushpuppies. saying macs or midwood smokehouse serves bbq is like saying mcdonalds serves burgers - they do. if bbq is meat with sauce on it and thousand island dressing is special sauce. old hickory house has those two beat.
also, if charlotte has so many great bbq restaurants why aren't any mentioned below. i also realized he ate at the airport, but the guy wasnt slamming bojangles.
yes - charlotte bbq sucks and every small town around here has at least two decent bbq joints. thats why i drive to lexington every week.
- November 27, 2012 at 10:35 PM
- Jim Mitchem said...
He's right, in one regard - we don't adhere to one specific 'style' of barbecue. In Texas it's consistent. In St. Louis. Memphis. Gainesville. All very consistent. No wavering. So yeah, we don't have a uniformed 'style' of barbecue here. But there are a few really great places - mostly uptown.
- November 27, 2012 at 10:42 PM
- Jimmy Dean said...
We have great 'que in the area, but I can't imagine airport food being a representation of anything but, well, airport food. Eastern and Western NC styles are represented along with SC style (mustard base sauce), however the authentic stuff will not be found in the newer BBQ restaurants around Charlotte. You have to go old school and seek out Old Hickory House on N. Tryon St., or BBQ King on Wilkinson Blvd., or Spoons on South Blvd.
- November 27, 2012 at 10:48 PM
- Anonymous said...
I don't know; What's Franklin Graham's take on all of this?
- November 28, 2012 at 8:01 AM
- Anonymous said...
Thanks for pointing out my error, Anon 6:59. You're absolutely right, I was working on deadline and didn't grab an atlas when I should. I was thinking of all that great food in Baltimore and got distracted by thoughts of crab cakes.
- November 28, 2012 at 8:14 AM
- Lee Ivester said...
The only thing Charlotte has to offer in the way of barbecue is I85...to Lexington.
- November 28, 2012 at 9:15 AM
- Anonymous said...
Q in Carlotte is horrible. People here would eat chopped spam covered in masterpiece sauce if it were called bbq.
Lexinton is the best close local for good Q.
- November 28, 2012 at 12:20 PM
- Father and Son Electric Service Co., Inc. said...
The best barbecue in the world can be found at a little place in Fredericksburg Virginia. Alman's Barbecue is on Rt #1 Jefferson Davis Hwy. in Fredericksburg. If you can ever get to go to this little place you will remember it forever. The meat melts in your mouth and the cole slaw is to die for. They give you a plate full of meat. Best in world, I am telling you.
- November 28, 2012 at 4:12 PM
- Anonymous said...
Please consider the source. This guy wrote for the American Way mag many years until he was let go in 2008. Worst writer ever. Even with hours to kill on long flights, it was more entertaining to read the Sky Mall or watch the peek-a-boo baby in the row ahead.
- November 28, 2012 at 5:47 PM
- sgibbsdesign said...
Never judge a cities food by the airport. Yes Charlotte has been a wasteland of BBQ but it has started to get some very good BBQ restaurants. I have had Mac's BBQ and didn't enjoy it, their competition Q is great but at their restaurants it's mediocre at best. Uptown, there is Queen City Q and it is good. Midtown Smokehouse is another good one and there are a few others growing up. Out side the city there are others like Ranucci's in Gastonia and 521 BBQ in Indian Land. The BBQ climate is changing for the better but it takes time. Most of the restaurants don't cater to eastern or western Carolina style BBQ but let the customer decide. Airports don't have the ability to smoke the BBQ properly on site. They may be able to warm it up but that just makes good BBQ ok. The best BBQ will always be found in your own backyard or at a competition.
- November 28, 2012 at 9:02 PM


text:
The Most Underused Compiler Switches in Visual C++, March 11, 2014 Microsoft's Visual C++ team explains the nine most underused switches and why you should make sure to include them in your build.
It's no secret that the Visual C++ team at Microsoft shares its engineering talent with ISVs and large customers to help them get the most out of the company's development tools. From this work, in which the engineering teams truly see everything from the sublime to the ridiculous, they gather information about how to improve the products, enhance recommended best practices, and refine their own consulting capabilities.
Who better, then, to discuss which useful switches are most often forgotten or even completely overlooked? Ankit Asthana, a program manager, and Ayman Shoukry, a principal program manager lead both from the Visual C++ team offered their top nine underused switches. We've included them here with text adapted from Microsoft's documentation followed by the authors' commentary on the switches. Predictably, many of them focus on performance optimization (the first seven switches), while the last few target enhancements to the build cycle itself. Ed.


text:
Courtesy of NewsMax
1. How long can they wait? President Barack Obama and Gov. Mitt pulled off the campaign trail — with a week to go before Election Day — because of the superstorm, both mindful of needing to put safety over politics. But, with the clock ticking, the longer they're off the road, the more they risk their ability to make a closing argument to on-the-fence voters in a race that polls show is tight.
2. How bad will it get? The destruction of Sandy on the East Coast has the potential to alter how, when and whether people can vote in the run-up to Nov. 6 and on Election Day itself. The storm also will affect voters in ways that are closer to home, like whether they and their families are safe. The campaign will probably be a background issue for many.
3. Delayed jobs report? The superstorm could complicate Friday's scheduled release of the October U.S. jobs report, the final snapshot of employment before the presidential election. Labor Department officials are hopeful they can release the report as scheduled at 8:30 a.m. Friday. But they acknowledged Monday that the storm could cause a delay.
4. What's Romney's path to 270? The Republican nominee and his allies are pushing into traditionally Democratic territory of Minnesota and Pennsylvania. But that flirting — along with Romney's increasingly narrow focus on Iowa, Wisconsin and Ohio — suggested he was still searching for a breakthrough in the Midwest to deny Obama the 270 Electoral College votes needed for victory.
5. A polling challenge: With millions on the East Coast potentially affected by floods, lost power or heavy snows from the superstorm, pollsters tracking the presidential race will have a hard time getting voters to answer their phones, if their phones are even working. Gallup suspended its daily tracking poll, according to Frank Newport, the editor-in-chief of the poll, and will make decisions about polling the rest of the week day by day as the storm's effects become clearer.


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text:
Difference between revisions of "Bounded gaps between primes"
(→World records)
(→World records)
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|Line 268:
[http://math.mit.edu/~drew/admissible_22949_248970.txt 248,970] ([http://sbseminar.wordpress.com/2013/06/05/more-narrow-admissible-sets/#comment-23893 Sutherland])
[http://math.mit.edu/~drew/admissible_22949_248970.txt 248,970] ([http://sbseminar.wordpress.com/2013/06/05/more-narrow-admissible-sets/#comment-23893 Sutherland])
Revision as of 17:54, 13 June 2013
World records
- [math]H[/math] is a quantity such that there are infinitely many pairs of consecutive primes of distance at most [math]H[/math] apart. Would like to be as small as possible (this is a primary goal of the Polymath8 project).
- [math]k_0[/math] is a quantity such that every admissible [math]k_0[/math]-tuple has infinitely many translates which each contain at least two primes. Would like to be as small as possible. Improvements in [math]k_0[/math] lead to improvements in [math]H[/math]. (The relationship is roughly of the form [math]H \sim k_0 \log k_0[/math]; see the page on finding narrow admissible tuples.)
- [math]\varpi[/math] is a technical parameter related to a specialized form of the Elliott-Halberstam conjecture. Would like to be as large as possible. Improvements in [math]\varpi[/math] lead to improvements in [math]k_0[/math]. (The relationship is roughly of the form [math]k_0 \sim \varpi^{-3/2}[/math]; there is an active discussion on optimising these improvements here.) In more recent work, the single parameter [math]\varpi[/math] is replaced by a pair [math](\varpi,\delta)[/math] (in previous work we had [math]\delta=\varpi[/math]). Discussion on improving the values of [math](\varpi,\delta)[/math] is currently being held here. In this table, infinitesimal losses in [math]\delta,\varpi[/math] are ignored.
|[math]\varpi[/math] or [math](\varpi,\delta)[/math]
|14 May
|1/1,168 (Zhang)
|3,500,000 (Zhang)
|70,000,000 (Zhang)
|All subsequent work is based on Zhang's breakthrough paper.
|21 May
|63,374,611 (Lewko)
|Optimises Zhang's condition [math]\pi(H)-\pi(k_0) \gt k_0[/math]; can be reduced by 1 by parity considerations
|28 May
|59,874,594 (Trudgian)
|Uses [math](p_{m+1},\ldots,p_{m+k_0})[/math] with [math]p_{m+1} \gt k_0[/math]
|30 May
| 59,470,640 (Morrison)
58,885,998? (Tao)
59,093,364 (Morrison)
57,554,086 (Morrison)
|Uses [math](p_{m+1},\ldots,p_{m+k_0})[/math] and then [math](\pm 1, \pm p_{m+1}, \ldots, \pm p_{m+k_0/2-1})[/math] following [HR1973], [HR1973b], [R1974] and optimises in m
|31 May
| 2,947,442 (Morrison)
2,618,607 (Morrison)
| 48,112,378 (Morrison)
42,543,038 (Morrison)
42,342,946 (Morrison)
|Optimizes Zhang's condition [math]\omega\gt0[/math], and then uses an improved bound on [math]\delta_2[/math]
|1 Jun
|42,342,924 (Tao)
|Tiny improvement using the parity of [math]k_0[/math]
|2 Jun
|866,605 (Morrison)
|13,008,612 (Morrison)
|Uses a further improvement on the quantity [math]\Sigma_2[/math] in Zhang's analysis (replacing the previous bounds on [math]\delta_2[/math])
|3 Jun
|1/1,040? (v08ltu)
|341,640 (Morrison)
| 4,982,086 (Morrison)
4,802,222 (Morrison)
|Uses a different method to establish [math]DHL[k_0,2][/math] that removes most of the inefficiency from Zhang's method.
|4 Jun
| 1/224?? (v08ltu)
1/240?? (v08ltu)
| 4,801,744 (Sutherland)
4,788,240 (Sutherland)
|Uses asymmetric version of the Hensley-Richards tuples
|5 Jun
|34,429? (Paldi/v08ltu)
| 4,725,021 (Elsholtz)
4,717,560 (Sutherland)
397,110? (Sutherland)
4,656,298 (Sutherland)
389,922 (Sutherland)
388,310 (Sutherland)
388,284 (Castryck)
388,248 (Sutherland)
387,982 (Castryck)
387,974 (Castryck)
| [math]k_0[/math] bound uses the optimal Bessel function cutoff. Originally only provisional due to neglect of the kappa error, but then it was confirmed that the kappa error was within the allowed tolerance.
[math]H[/math] bound obtained by a hybrid Schinzel/greedy (or "greedy-greedy") sieve
|6 Jun
| 387,960 (Angelveit)
387,904 (Angeltveit)
|Improved [math]H[/math]-bounds based on experimentation with different residue classes and different intervals, and randomized tie-breaking in the greedy sieve.
|7 Jun
[math]207 \varpi + 43\delta \lt \frac{1}{4}[/math] (v08ltu/Green)
26,024? (vo8ltu)
387,534 (pedant-Sutherland)
|Many of the results ended up being retracted due to a number of issues found in the most recent preprint of Pintz.
|June 8
| 286,224 (Sutherland)
285,752 (pedant-Sutherland)
|values of [math]\varpi,\delta,k_0[/math] now confirmed; most tuples available on dropbox. New bounds on [math]H[/math] obtained via iterated merging using a randomized greedy sieve.
|Jun 9
|181,000*? (Pintz)
|2,530,338*? (Pintz)
|New bounds on [math]H[/math] obtained by interleaving iterated merging with local optimizations.
|Jun 10
|23,283? (Harcos/v08ltu)
|285,210 (Sutherland)
|More efficient control of the [math]\kappa[/math] error using the fact that numbers with no small prime factor are usually coprime
|Jun 11
|252,804 (Sutherland)
| More refined local "adjustment" optimizations, as detailed here.
An issue with the [math]k_0[/math] computation has been discovered, but is in the process of being repaired.
|Jun 12
| 22,951 (Tao/v08ltu)
22,949 (Harcos)
|249,180 (Castryck)
|Improved bound on [math]k_0[/math] avoids the technical issue in previous computations.
|Jun 13
- ? - unconfirmed or conditional
- ?? - theoretical limit of an analysis, rather than a claimed record
- * - is majorized by an earlier but independent result
- strikethrough - values relied on a computation that has now been retracted
See also the article on Finding narrow admissible tuples for benchmark values of [math]H[/math] for various key values of [math]k_0[/math].
Polymath threads
- I just can't resist: there are infinitely many pairs of primes at most 59470640 apart, Scott Morrison, 30 May 2013. Inactive
- The prime tuples conjecture, sieve theory, and the work of Goldston-Pintz-Yildirim, Motohashi-Pintz, and Zhang, Terence Tao, 3 June 2013. Inactive
- Polymath proposal: bounded gaps between primes, Terence Tao, 4 June 2013. Active
- Online reading seminar for Zhang's "bounded gaps between primes, Terence Tao, 4 June 2013. Active
- More narrow admissible sets, Scott Morrison, 5 June 2013. Active
- The elementary Selberg sieve and bounded prime gaps, Terence Tao, 8 June 2013. Inactive
- A combinatorial subset sum problem associated with bounded prime gaps, Terence Tao, 10 June 2013. Active
- Further analysis of the truncated GPY sieve, Terence Tao, 11 June 2013. Active
Code and data
- Hensely-Richards sequences, Scott Morrison
- A mathematica notebook for finding k_0, Scott Morrison
- python implementation, Avi Levy
- k-tuple pattern data, Thomas J Engelsma
- Sifted sequences, Vit Tucek
- Other sifted sequences, Christian Elsholtz
- Size of largest admissible tuples in intervals of length up to 1050, Clark and Jarvis
- C implementation of the "greedy-greedy" algorithm, Andrew Sutherland
- Dropbox for sequences, pedant
- Spreadsheet for admissible sequences, Vit Tucek
- Java code for optimising a given tuple V1.0, Java code for optimising a given tuple V1.1, xfxie
Page numbers refer to the file linked to for the relevant paper.
- Errata for Zhang's "Bounded gaps between primes"
- Page 5: In the first display, [math]\mathcal{E}[/math] should be multiplied by [math]\mathcal{L}^{2k_0+2l_0}[/math], because [math]\lambda(n)^2[/math] in (2.2) can be that large, cf. (2.4).
- Page 14: In the final display, the constraint [math](n,d_1=1[/math] should be [math](n,d_1)=1[/math].
- Page 35: In the display after (10.5), the subscript on [math]{\mathcal J}_i[/math] should be deleted.
- Page 36: In the third display, a factor of [math]\tau(q_0r)^{O(1)}[/math] may be needed on the right-hand side (but is ultimately harmless).
- Page 38: In the display after (10.14), [math]\xi(r,a;q_1,b_1;q_2,b_2;n,k)[/math] should be [math]\xi(r,a;k;q_1,b_1;q_2,b_2;n)[/math].
- Page 42: In (12.3), [math]B[/math] should probably be 2.
- Page 47: In the third display after (13.13), the condition [math]l \in {\mathcal I}_i(h)[/math] should be [math]l \in {\mathcal I}_i(sh)[/math].
- Page 49: In the top line, a comma in [math](h_1,h_2;,n_1,n_2)[/math] should be deleted.
- Page 51: In the penultimate display, one of the two consecutive commas should be deleted.
- Page 54: Three displays before (14.17), [math]\bar{r_2}(m_1+m_2)q[/math] should be [math]\bar{r_2}(m_1+m_2)/q[/math].
- Errata for Motohashi-Pintz's "A smoothed GPY sieve"
- Page 31: The estimation of (5.14) by (5.15) does not appear to be justified. In the text, it is claimed that the second summation in (5.14) can be treated by a variant of (4.15); however, whereas (5.14) contains a factor of [math](\log \frac{R}{|D|})^{2\ell+1}[/math], (4.15) contains instead a factor of [math](\log \frac{R/w}{|K|})^{2\ell+1}[/math] which is significantly smaller (K in (4.15) plays a similar role to D in (5.14)). As such, the crucial gain of [math]\exp(-k\omega/3)[/math] in (4.15) does not seem to be available for estimating the second sum in (5.14).
- Errata for Pintz's "A note on bounded gaps between primes"
- Page 7: In (2.39), the exponent of [math]3a/2[/math] should instead be [math]-5a/2[/math] (it comes from dividing (2.38) by (2.37)). This impacts the numerics for the rest of the paper.
- Page 8: The "easy calculation" that the relative error caused by discarding all but the smooth moduli appears to be unjustified, as it relies on the treatment of (5.14) in Motohashi-Pintz which has the issue pointed out in 2.1 above.
Other relevant blog posts
- Marker lecture III: "Small gaps between primes", Terence Tao, 19 Nov 2008.
- The Goldston-Pintz-Yildirim result, and how far do we have to walk to twin primes ?, Emmanuel Kowalski, 22 Jan 2009.
- Number Theory News, Peter Woit, 12 May 2013.
- Bounded Gaps Between Primes, Emily Riehl, 14 May 2013.
- Bounded gaps between primes!, Emmanuel Kowalski, 21 May 2013.
- Bounded gaps between primes: some grittier details, Emmanuel Kowalski, 4 June 2013.
- Bound on prime gaps bound decreasing by leaps and bounds, Christian Perfect, 8 June 2013.
- Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture, 20 May 2013.
- A technical question related to Zhang's result of bounded prime gaps, 25 May 2013.
- How does Yitang Zhang use Cauchy's inequality and Theorem 2 to obtain the error term coming from the [math]S_2[/math] sum, 31 May 2013.
- Tightening Zhang's bound, 3 June 2013.
- Does Zhang's theorem generalize to 3 or more primes in an interval of fixed length?, 3 June 2013.
Wikipedia and other references
- Bessel function
- Bombieri-Vinogradov theorem
- Brun-Titchmarsh theorem
- Dispersion method
- Prime gap
- Second Hardy-Littlewood conjecture
- Twin prime conjecture
Recent papers and notes
- On the exponent of distribution of the ternary divisor function, Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, 11 Apr 2013.
- On the optimal weight function in the Goldston-Pintz-Yildirim method for finding small gaps between consecutive primes, Bálint Farkas, János Pintz and Szilárd Gy. Révész, To appear in: Paul Turán Memorial Volume: Number Theory, Analysis and Combinatorics, de Gruyter, Berlin, 2013. 23 pages. arXiv
- Bounded gaps between primes, Yitang Zhang, to appear, Annals of Mathematics. Released 21 May, 2013.
- Polignac Numbers, Conjectures of Erdös on Gaps between Primes, Arithmetic Progressions in Primes, and the Bounded Gap Conjecture, Janos Pintz, 27 May 2013.
- A poor man's improvement on Zhang's result: there are infinitely many prime gaps less than 60 million, T. S. Trudgian, 28 May 2013.
- The Friedlander-Iwaniec sum, É. Fouvry, E. Kowalski, Ph. Michel., May 2013.
- Notes on Zhang's prime gaps paper, Terence Tao, 1 June 2013.
- Bounded prime gaps in short intervals, Johan Andersson, 3 June 2013.
- Bounded length intervals containing two primes and an almost-prime II, James Maynard, 5 June 2013.
- A note on bounded gaps between primes, Janos Pintz, 6 June 2013.
- First proof that infinitely many prime numbers come in pairs, Maggie McKee, Nature, 14 May 2013.
- Proof that an infinite number of primes are paired, Lisa Grossman, New Scientist, 14 May 2013.
- Unheralded Mathematician Bridges the Prime Gap, Erica Klarreich, Simons science news, 20 May 2013.
- The article also appeared on Wired as "Unknown Mathematician Proves Elusive Property of Prime Numbers".
- The Beauty of Bounded Gaps, Jordan Ellenberg, Slate, 22 May 2013.
- Game of proofs boosts prime pair result by millions, Jacob Aron, New Scientist, 4 June 2013.
Additional links for some of these references (e.g. to arXiv versions) would be greatly appreciated.
- [BFI1986] Bombieri, E.; Friedlander, J. B.; Iwaniec, H. Primes in arithmetic progressions to large moduli. Acta Math. 156 (1986), no. 3-4, 203–251. MathSciNet Article
- [BFI1987] Bombieri, E.; Friedlander, J. B.; Iwaniec, H. Primes in arithmetic progressions to large moduli. II. Math. Ann. 277 (1987), no. 3, 361–393. MathSciNet Article
- [BFI1989] Bombieri, E.; Friedlander, J. B.; Iwaniec, H. Primes in arithmetic progressions to large moduli. III. J. Amer. Math. Soc. 2 (1989), no. 2, 215–224. MathSciNet Article
- [B1995] Jörg Brüdern, Einführung in die analytische Zahlentheorie, Springer Verlag 1995
- [CJ2001] Clark, David A.; Jarvis, Norman C.; Dense admissible sequences. Math. Comp. 70 (2001), no. 236, 1713–1718 MathSciNet Article
- [FI1981] Fouvry, E.; Iwaniec, H. On a theorem of Bombieri-Vinogradov type., Mathematika 27 (1980), no. 2, 135–152 (1981). MathSciNet Article
- [FI1983] Fouvry, E.; Iwaniec, H. Primes in arithmetic progressions. Acta Arith. 42 (1983), no. 2, 197–218. MathSciNet Article
- [FI1985] Friedlander, John B.; Iwaniec, Henryk, Incomplete Kloosterman sums and a divisor problem. With an appendix by Bryan J. Birch and Enrico Bombieri. Ann. of Math. (2) 121 (1985), no. 2, 319–350. MathSciNet JSTOR
- [GPY2009] Goldston, Daniel A.; Pintz, János; Yıldırım, Cem Y. Primes in tuples. I. Ann. of Math. (2) 170 (2009), no. 2, 819–862. arXiv MathSciNet
- [GR1998] Gordon, Daniel M.; Rodemich, Gene Dense admissible sets. Algorithmic number theory (Portland, OR, 1998), 216–225, Lecture Notes in Comput. Sci., 1423, Springer, Berlin, 1998. MathSciNet Article
- [HR1973] Hensley, Douglas; Richards, Ian, On the incompatibility of two conjectures concerning primes. Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972), pp. 123–127. Amer. Math. Soc., Providence, R.I., 1973. MathSciNet Article
- [HR1973b] Hensley, Douglas; Richards, Ian, Primes in intervals. Acta Arith. 25 (1973/74), 375–391. MathSciNet Article
- [MP2008] Motohashi, Yoichi; Pintz, János A smoothed GPY sieve. Bull. Lond. Math. Soc. 40 (2008), no. 2, 298–310. arXiv MathSciNet Article
- [MV1973] Montgomery, H. L.; Vaughan, R. C. The large sieve. Mathematika 20 (1973), 119–134. MathSciNet Article
- [M1978] Hugh L. Montgomery, The analytic principle of the large sieve. Bull. Amer. Math. Soc. 84 (1978), no. 4, 547–567. MathSciNet Article
- [R1974] Richards, Ian On the incompatibility of two conjectures concerning primes; a discussion of the use of computers in attacking a theoretical problem. Bull. Amer. Math. Soc. 80 (1974), 419–438. MathSciNet Article
- [S1961] Schinzel, A. Remarks on the paper "Sur certaines hypothèses concernant les nombres premiers". Acta Arith. 7 1961/1962 1–8. MathSciNet Article
- [S2007] K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yıldırım. Bull. Amer. Math. Soc. (N.S.) 44 (2007), no. 1, 1–18. MathSciNet Article arXiv