We've found 8,914 results for “

Patek Philippe


Our Most Popular Models


View

Sort by

Patek Philippe Rose gold 36mmmm Automatic 3940R-011 pre-owned United States of America, New York, New York
TOP
Patek Philippe 3940R-011 Perpetual Calendar, Rose Gold, Complete
$59,900
Professional dealer
13
US
Patek Philippe Platinum 34.5mm Automatic 5738P-001 new United States of America, New York, New York
TOP
Patek Philippe 5738P-001 Blue Golden Ellipse NEW
$48,500
Free shipping
Professional dealer
485
US
Patek Philippe Rose gold 35mm Manual winding Calatrava pre-owned United States of America, New York, New York, New York
TOP
Patek Philippe Rare 1578 SPIDER lug 1943 PINK Gold & Pink Dial...
$32,000
Free shipping
Professional dealer
38
US
Patek Philippe Steel 41mm Automatic 5726/1A-014 new United States of America, New York, New York
TOP
Patek Philippe Nautilus Stainless Steel Annual Calendar Blue...
$127,299
Free shipping
Professional dealer
337
US
Patek Philippe Rose gold 36mm Manual winding 5119R-001 pre-owned United States of America, California, Pasadena
TOP
Patek Philippe Calatrava with Box and Papers MINT Rose Gold 5119R
$18,242
Professional dealer
47
US
Patek Philippe Yellow gold 36mm Manual winding 3970 J new United States of America, New York, Westchester
Patek Philippe Perpetual Calendar Chronograph
$105,000
Professional dealer
6
US
Patek Philippe Steel 40mm Automatic 5711/1A-010 pre-owned United States of America, New York, NEW YORK
TOP
Patek Philippe Nautilus Blue Dial 5711/1A-010
$95,500
Free shipping
Professional dealer
178
US
Patek Philippe Platinum 41mm Manual winding 5271P-001 new United States of America, Florida, Miami
Patek Philippe Perpetual Calendar
$279,295
Professional dealer
 
US
Patek Philippe Steel 35.2mm Automatic 7118/1A-011 pre-owned United States of America, Arizona, Scottsdale
Patek Philippe Nautilus
$41,500
Professional dealer
5
US
Patek Philippe Rose gold 36mm Automatic 7300/1201R-010 new United States of America, Georgia, Alpharetta
Patek Philippe Twenty 4 Automatic Self Winding (Chocolate)
$47,299
Free shipping
Professional dealer
325
US
Patek Philippe Yellow gold 33mm Manual winding 3960J pre-owned United States of America, Massachusetts, Boston
Patek Philippe Calatrava Half Hunter Officer Case Celebrating...
$15,999
Professional dealer
157
US
Patek Philippe Rose gold 42mm Automatic 5905R-001 new United States of America, California, Beverly Hills
Patek Philippe Annual Calendar Chronograph
$64,950
Professional dealer
141
US
Patek Philippe Steel 37mm Automatic 3800/1 pre-owned United States of America, California, Beverly Hills
Patek Philippe Steel Nautilus Watch Ref. 3800
$45,000
Professional dealer
86
US
Patek Philippe Steel 40mm Automatic 5167 pre-owned United States of America, Illinois, BUFFALO GROVE
Patek Philippe Aquanaut Stainless Steel On Bracelet 5167/1a-001
$49,750
Free shipping
Professional dealer
262
US
Patek Philippe Yellow gold 35.5mm Manual winding 1463 pre-owned United States of America, New York, Armonk
Patek Philippe Chronograph
$130,000
Professional dealer
6
US
Patek Philippe Steel 40.5mm Automatic 5726/1A-001 pre-owned United States of America, New York, NEW YORK
TOP
Patek Philippe Nautilus Annual Calendar Moon Phase Grey Dial...
$102,000
Free shipping
Professional dealer
178
US
Patek Philippe White gold 44mm Automatic 5976/1G-001 new United States of America, Florida, Miami
Patek Philippe Nautilus
$449,985
Professional dealer
 
US
Patek Philippe Steel 25mm Quartz 4910/10A-012 pre-owned United States of America, Arizona, Scottsdale
Patek Philippe Twenty-4
$12,500
Professional dealer
5
US
Patek Philippe Rose gold 28mm Manual winding 448R new United States of America, California, Los Angeles
Patek Philippe 448R Calatrava Watch
$12,950
Professional dealer
16
US
Patek Philippe Rose gold 41mm Manual winding 5270R-001 new United States of America, New York, NY
Patek Philippe 5270R-001 Perpetual Calendar Chronograph
$145,950
Professional dealer
18
US
Patek Philippe Rose gold 40mm Automatic 5711R new United States of America, California, Beverly Hills
Patek Philippe Nautilus
$89,950
Professional dealer
141
US
Patek Philippe Yellow gold 39mm Automatic 5146J-010 pre-owned United States of America, California, Beverly Hills
Patek Philippe Yellow Gold Annual Calendar Watch Ref. 5146
$29,500
Professional dealer
86
US
Patek Philippe Steel 40mm Automatic 5167A-001 pre-owned United States of America, Illinois, chicago
TOP
Patek Philippe Aquanaut
$43,003
Private Seller
 
US
Patek Philippe Rose gold 37mm Manual winding 2458 new United States of America, New York, Westchester
Patek Philippe Calatrava Ref 2458 R
$27,850
Professional dealer
6
US
Patek Philippe White gold 39mm Automatic 5146G-010 new United States of America, New York, NEW YORK
TOP
Patek Philippe Annual Calendar 5146G-010
$37,500
Free shipping
Professional dealer
178
US
Patek Philippe Steel 40.5mm Automatic 5726/1A-010 new United States of America, Florida, Miami
Patek Philippe Nautilus Tiffany & CO. RARE SET
$239,885
Professional dealer
 
US
Patek Philippe Steel 42.2mm Automatic 5968A-001 new United States of America, New York, New York
Patek Philippe Aquanaut Stainless Steel 42mm 5968A-001
$135,200
Free shipping
Professional dealer
94
US
Patek Philippe Rose gold 25mm Quartz 4910/11R-010 pre-owned United States of America, Arizona, Scottsdale
Patek Philippe Twenty-4
$25,500
Professional dealer
5
US
Patek Philippe White gold 40mm Automatic 5740/1G-001 new United States of America, New York, NY
Patek Philippe 5740/1G-001 Nautilus
$227,950
Professional dealer
18
US
Patek Philippe Steel 40.5mm Automatic 5980/1A-001 new United States of America, California, Beverly Hills
Patek Philippe Nautilus
$169,500
Professional dealer
141
US
Patek Philippe Yellow gold 37mm Automatic 3800/1 pre-owned United States of America, California, Beverly Hills
Patek Philippe Yellow Gold Nautilus Watch Ref. 3800
$55,000
Professional dealer
86
US
Patek Philippe Platinum 40mm Automatic 5960P pre-owned United States of America, Illinois, BUFFALO GROVE
Patek Philippe ANNUAL CALENDAR CHRONOGRAPH PLATINUM 40MM 5960P...
$50,750
Free shipping
Professional dealer
262
US
Patek Philippe Steel 38.4mm Automatic 5800/1A-001 pre-owned United States of America, New York, Westchester County
Patek Philippe Nautilus
$104,225
Professional dealer
6
US
Patek Philippe Rose gold 42mm Automatic 5524R-001 new United States of America, New York, NEW YORK
TOP
Patek Philippe Travel Time Rose Gold Calatrava Pilot
$43,500
Free shipping
Professional dealer
178
US
Patek Philippe White gold 40.8mm Automatic 5650G-001 new United States of America, Florida, Miami
Patek Philippe Travel Time Advanced Research Aquanaut
$389,985
Professional dealer
 
US
Patek Philippe Yellow gold 33mm Manual winding 3520J pre-owned United States of America, Maryland, Baltimore, MD
Patek Philippe Calatrava
$8,939
Professional dealer
392
US
Patek Philippe Yellow gold 33mm Manual winding Calatrava pre-owned United States of America, Florida, Sarasota
TOP
Patek Philippe Calatrava 2557 18K Yellow Gold Manual 33mm...
$6,250
Professional dealer
327
US
Patek Philippe Steel 40.8mm Automatic 5164A-001 new United States of America, New York, NY
Patek Philippe 5164A-001 Aquanaut
$83,500
Professional dealer
18
US
Patek Philippe Rose gold 37mm Automatic 5107R-001 new United States of America, California, Beverly Hills
Patek Philippe Calatrava Rose Gold 37mm Silver Dial
$19,850
Professional dealer
141
US
Patek Philippe Yellow gold 36mm Automatic 3940J F pre-owned United States of America, California, Beverly Hills
Patek Philippe Yellow Gold Perpetual Calendar First Series...
$48,000
Professional dealer
86
US
Patek Philippe White gold 37mm Automatic 5036/1G pre-owned United States of America, Illinois, BUFFALO GROVE
Patek Philippe 5036/1G White Gold 37mm box and archive papers
$36,750
Free shipping
Professional dealer
262
US
Patek Philippe Platinum 42mm Manual winding 2461 pre-owned United States of America, New York, Westchester
Patek Philippe 2461 P
$24,000
Professional dealer
6
US
Patek Philippe Steel 40mm Automatic 5712/1A-001 pre-owned United States of America, New York, NEW YORK
TOP
Patek Philippe Nautilus 5712/1A-001
$99,000
Free shipping
Professional dealer
178
US
Patek Philippe White gold 40mm Automatic 5722G-001 pre-owned United States of America, Florida, Miami
Patek Philippe Nautilus
$185,895
Professional dealer
 
US
Patek Philippe Yellow gold 29.5mm Manual winding 5500J pre-owned United States of America, Georgia, Atlanta
TOP
Patek Philippe Pagoda 5500J Watch with Leather Bracelet and...
$18,450
Free shipping
Professional dealer
968
US
Patek Philippe Steel 40mm Automatic 5711/1A-010 pre-owned United States of America, Florida, MIAMI
TOP
Patek Philippe Nautilus
$108,000
Private Seller
 
US
Patek Philippe Steel 40.5mm Automatic 5726/1A-014 new United States of America, New York, NY
Patek Philippe 5726/1A-014 Nautilus
$129,500
Professional dealer
18
US
Patek Philippe Rose gold 36mm Manual winding 3970ER pre-owned United States of America, California, Beverly Hills
Patek Philippe Perpetual Calendar Chronograph
$104,500
Professional dealer
141
US
Patek Philippe Yellow gold 37mm Automatic 5110J pre-owned United States of America, California, Beverly Hills
Patek Philippe World Time Yellow Gold Ref. 5110J
$27,500
Professional dealer
86
US
Patek Philippe White gold 42mm Automatic 5168G-001 pre-owned United States of America, Illinois, BUFFALO GROVE
Patek Philippe Aquanaut White Gold Blue Dial Rubber Strap 42mm...
$74,750
Free shipping
Professional dealer
262
US
Patek Philippe Platinum 37mm Manual winding 5134P-001 pre-owned United States of America, New York, Westchester County
Patek Philippe Travel Time
$28,500
Professional dealer
6
US
Patek Philippe Yellow gold 30.5mm Manual winding 96J pre-owned United States of America, California, Los Angeles
Patek Philippe 96J Original Calatrava Watch Circa 1956
$16,000
Professional dealer
16
US
Patek Philippe Rose gold 40.5mm Automatic 5980/1R-001 new United States of America, Florida, Miami
Patek Philippe Nautilus
$229,895
Professional dealer
 
US
Patek Philippe White gold 40mm Automatic 5711G-001 pre-owned United States of America, New York, New York
Patek Philippe Nautilus White Gold 5711G-001
$67,600
Free shipping
Professional dealer
94
US
Patek Philippe Yellow gold 36mm Automatic Vintage new United States of America, California, Malibu
Patek Philippe Vintage 3604 Full Set
$20,000
Free shipping
Professional dealer
10
US
Patek Philippe Yellow gold 38.5mm Automatic 5231J-001 new United States of America, New York, NY
Patek Philippe 5231j-001 World Time
$107,500
Professional dealer
18
US
Patek Philippe Yellow gold 36mm Manual winding 3970E pre-owned United States of America, California, Beverly Hills
Patek Philippe Perpetual Calendar Chronograph
$89,500
Professional dealer
141
US
Patek Philippe Platinum 38mm Automatic 5077P-089 new United States of America, California, Beverly Hills
Patek Philippe Platinum Handcrafts Cloisonne Watch, Ref. 5077...
$128,000
Professional dealer
86
US
Patek Philippe White gold 30mm Manual winding 5024G pre-owned United States of America, Illinois, BUFFALO GROVE
Patek Philippe Gondolo White Gold Salmon Dial Alligator Strap...
$11,250
Free shipping
Professional dealer
262
US
Patek Philippe White gold 37mm Automatic 4936G pre-owned United States of America, New York, NY
Patek Philippe ANNUAL CALENDAR 37MM 4936G 18K WHITE GOLD MEN'S...
$31,500
Professional dealer
118
US
Patek Philippe Rose gold 31mm Manual winding 3796R pre-owned United States of America, California, Los Angeles
Patek Philippe 3796R Classic Calatrava Watch
$15,000
Professional dealer
16
US
Patek Philippe Rose gold 40mm Automatic 5724R-001 new United States of America, Florida, Miami
Patek Philippe Nautilus
$254,985
Professional dealer
 
US
Patek Philippe Rose gold Automatic 5712R-001 new United States of America, New York, New York
Patek Philippe Nautilus Moon Phase 18K Rose Gold 5712R-001
$85,280
Free shipping
Professional dealer
94
US
Patek Philippe Rose gold 40mm Automatic 5712R-001 pre-owned United States of America, Texas, Houston
TOP
Patek Philippe Nautilus
$78,500
Private Seller
 
US

Patek Philippe: Prestige Par Excellence

No other name represents haute horlogerie like Patek Philippe. This Genevan manufacturer unites luxury, tradition, and high-quality craftsmanship in some of the world's most exquisite watches. Their watches are both status symbols and investments.


5 Reasons to Buy a Patek Philippe

  • First choice of famous politicians, athletes, and actors
  • Great investments: the Calatrava dress watch and Nautilus sports watch
  • Gold and platinum used as the primary case materials
  • Modern in-house calibers for high precision
  • Inventor of many important complications such as the perpetual calendar and split-seconds chronograph

Independent and Highly Esteemed

Patek Philippe are one of the few remaining independent Genevan watch manufacturers. They are still family owned, which contributes to their good reputation — and not just among experts. Patek Philippe build nearly every component for their watches themselves. A Patek Philippe is the crowning piece of any watch collector's collection. What's more, their high esteem and lasting value make these timepieces fantastic investments.

This Geneva-based manufacturer offers over 200 unique watch models. Their style tends to be more on the conservative side. While stainless steel models are available, Patek Philippe use platinum and white, yellow, and rose gold more than many other manufacturers.

Two of the most famous collections from this storied company are the Calatrava and the Nautilus. The former has been part of the Patek catalog since 1932. This collection draws its inspiration from the simple and linear style of Bauhaus design. Its name comes from the Order of Calatrava, whose cross serves as the company logo. This same image also adorns the crown of each Patek watch.

On the other hand, the Nautilus impresses with its sporty and dynamic design. Famous watch designer Gerald Génta designed this watch. Previously, Génta had attracted plenty of attention for designing the Audemars Piguet Royal Oak.

Patek Philippe flexes their watchmaking muscles in the Complications and Grand Complications collections. Here you'll find watches with tourbillons, chimes, perpetual calendars, moon phase displays, and world time functions.


How much do watches from Patek Philippe cost?

Model Price (approx.) Features
Grand Complications 5304R 583,000 USD Minute repeater, perpetual calendar, moon phase, rose gold
World Time 5131/1P 176,000 USD World time, day/night display, platinum
Gondolo 7099R 93,300 USD Barrel-shaped, diamonds, rose gold
Nautilus 5990/1A 70,000 USD Chronograph, second time zone, day/night display, stainless steel
Nautilus 5711/1A 52,500 USD Date, stainless steel
Aquanaut 5167/1A 29,100 USD Date, stainless steel
Calatrava 5227R 28,600 USD Date, rose gold
Calatrava 5119G 16,100 USD Small seconds, white gold, manual
Golden Ellipse 4226R 5,200 USD Rose gold, manual

The Calatrava: A Timeless Classic

The Calatrava collection has been part of the Patek Philippe catalog for over 80 years. Thanks to its simple elegance, it is the perfect companion to any tailor-made suit and, thus, the ideal dress watch. There are a number of models to choose from. Models with a small seconds dial at 6 feel particularly elegant. The use of manual calibers also allows these timepieces to stay rather thin. You can purchase a well-maintained watch in yellow gold for as little as 9,800 USD. New pieces range in price from 16,100 to 22,700 USD.

You can also get the Calatrava with an automatic movement. Most of these models feature a central second hand and a date at 3 o'clock. Pre-owned models in good condition cost between 19,200 and 25,200 USD. You'll need to invest anywhere from 22,700 to 28,800 USD for a never-worn example. The finest variants of the Calatrava have intricately engraved dials and cases made of platinum. Such timepieces easily demand over 117,000 USD.


Sporty and Modern: The Nautilus and the Aquanaut

Patek Philippe show off their sporty side with the Nautilus. Those who value tradition gravitate toward the models in stainless steel—the material used for the very first Nautilus. It was released in 1976 under the reference number 3700/1 and drew immediate attention with its porthole design. Today, these vintage models cost a solid 81,600 USD. Its successor, the ref. 5711/1, changes hands for around 50,100 USD pre-owned. Never-worn examples cost an additional 2,900 USD.

However, Patek Philippe not only offers the Nautilus as a three-hand watch, but also with complications, including annual calendars, moon phase indicators, chronographs, and second time zones. Depending on the complication, expect to pay between 45,500 and 104,000 USD for one of these timepieces. The most expensive Nautilus is a 33-mm women's model in white gold. It is encrusted with over 1,700 diamonds and sells for around 218,000 USD new.

In 1997, Patek released a watch clearly inspired by the Nautilus — the Aquanaut. That said, it is by no means a replica: Its design is more modern and less angular. The so-called "tropical" strap is made of a special composite material that is resistant to water, abrasion, and UV radiation. Prices for the three-hand version in stainless steel come in at around 29,200 USD. Those in white or rose gold are more expensive at about 35,100 USD. Be prepared to invest another 5,800 USD if you choose a model with a chronograph function or second time zone.

Women's models in the Aquanaut collection come with the choice of a quartz or automatic caliber. A 35.6-mm quartz timepiece costs 14,600 USD in stainless steel with diamonds on the bezel. The rose gold version with an automatic caliber sells for around 35,100 USD.


High Class: Complications and Grand Complications

Patek Philippe turn watchmaking into an art form in the Complications and Grand Complications collections. Watch enthusiasts are sure to get their money's worth — assuming they have the necessary funds. Relatively speaking, models featuring an annual calendar and moon phase indicator are rather affordable, with prices of between 35,000 and 47,000 USD. World time watches, those with a tourbillon, and pieces with finely skeletonized and decorated movements come in at about 93,500 USD. You'll have to dig much deeper into your pockets if you want one of the intricately finished top models with a minute repeater and perpetual calendar. Prices for these masterpieces usually range from 175,000 to 585,000 USD.


Anything but Round: Golden Ellipse, Gondolo, and Twenty~4

In addition to the classically round Calatrava and the porthole design of the Nautilus, Patek Philippe also offer a wide array of watches in different shapes. For example, the Golden Ellipse catches the eye with its elliptical design. Crafted according to the divine proportion, it exudes a classic beauty. Current models come in platinum or rose gold and cost around 42,100 USD. However, you can find older models from the 1970s and 80s for as little as 5,300 to 7,000 USD.

Patek Philippe had women in mind when creating the Twenty~4 collection. This watch has a rectangular case and bears a slight resemblance to the Cartier Tank thanks to its integrated bracelet and Roman numerals. The Twenty~4 is only available as a quartz watch and comes in stainless steel or rose gold. Plan to spend anywhere from 8,200 to 35,100 USD on this timepiece.

The Gondolo collection is marked by its Art Deco design and interesting shapes. Whether it's pillow-shaped, rectangular, barrel-shaped, or a subtle combination of the three, this collection has something for everyone. Patek produce these watches exclusively in gold, which is then artfully combined with diamonds and pearls. Most are powered by manual calibers, though some feature a quartz movement. Simpler models cost around 17,000 USD. Prices for more intricate pieces with diamonds and pearls can easily reach up to 170,000 USD.


Modern Caliber Technology, Unique Quality Seal

Patek Philippe also feature a few watches with quartz movements. The manufacturer even invented the first so-called solid-state quartz watch with no moving parts and had it patented in 1959.

However, Patek Philippe are better known for mechanical watches made with in-house movements. Their calibers have a few special features. In 1949, the company patented the "Gyromax," a special type of balance wheel that is still in use today. While regular balance wheels feature weight adjustment screws on the outside of the rim, the Gyromax has weights set in it. Therefore, it has a greater moment of inertia, resulting in increased precision. Patek Philippe have used the material Silinvar in their escapements since 2005. Similar to silicon, it's anti-magnetic and extremely hard. Due to this hardness, there is less friction in the movement and it doesn't require lubrication. The manufacturer presented the first balance spring made from this high-tech material in 2006.

Over the years, Patek Philippe have continued to scale back the number of outsourced movements and components in their watches. In 2005, the company introduced their first in-house chronograph caliber. Since 2012, they have been producing all their chronograph movements themselves. Before that, they had used movements from other manufacturers. For example, the first Nautilus used a caliber based on the 920 by Jaeger-LeCoultre. Audemars Piguet used this movement for the first Royal Oak as well, as did Vacheron Constatin for the 222. Valjoux and Lemania also used to deliver to Patek Philippe.

In 2009, Patek Philippe introduced and began using their own seal, which marks a watch passing the world's most demanding quality test for mechanical timepieces. They had previously used the Geneva Seal, which has been a sign of high-quality watches from that canton since 1886. A significant difference between the two is that the new testing methods are for the entire, finished watch. According to the old Geneva Seal rules, separate movements could receive certificates.


The Inventor of the Crown

In 1839, Polish watchmaker and emigrant Antoni Patek (1811-1877) began producing pocket watches in Geneva. There, in 1845, he combined forces with his French colleague Adrien Philippe (1815-1894). Philippe's father had been a watchmaker and taught his son the craft. In 1844, Philippe unveiled an invention to the world of watches that is ubiquitous today: the crown. Before this, movements were usually wound using a key, much like many larger clocks today. The company has existed under the name Patek Philippe since 1851.

The two business partners participated in the Great Exhibition of 1851 in London, where Queen Victoria purchased two watches: one for herself, and one for Prince Albert. Danish and Italian royalty also became members of their distinguished clientele. In addition, a partnership with the New York jeweler Tiffany & Co. began during a trip to the United States when the American retailer ordered 130 watches. In 1902, Patek Philippe patented the first double chronograph and in 1925, they introduced the first wristwatch with a perpetual calendar. In 1932, the Stern family took over the business. Thierry Stern has been leading the company since 2010. Patek Philippe produces around 50,000 watches per year.

Queen Victoria wasn't the only British icon who appreciated Patek Philippe. Two of her great-great-granddaughter's most prominent subjects, Beatles members Paul McCartney and Ringo Starr, have an affinity for these watches. They have each been Aquanaut owners for some time, though Rolex's Submariner may have been more fitting for the musicians responsible for "Yellow Submarine." The Dalai Lama wears a Patek Philippe chronograph gifted to him by President Franklin Delano Roosevelt, and actor Brad Pitt wears a Nautilus.


A Rivalry Between Watch Collectors

Patek Philippe have always defined themselves by their excellence. In 1933, after three years of development and five years of manufacturing, the Henry Graves Supercomplication, an 18-karat gold timepiece, was finally completed. Banker Henry Graves Jr. had commissioned the watch in order to outdo the pocket watches commissioned by automaker James Ward Packard. Packard owned a dozen complicated Patek Philippe timepieces, which he had collected over the course of 25 years.

Graves and Packard were two of the leading watch collectors of their time and had an ongoing rivalry that the Supercomplication ended. The watch is composed of 920 individual components and has 24 impressive complications. These include a perpetual calendar, Westminster Quarters, the sunrise and sunset time, and a view of the starry sky over New York City from Graves' Fifth Avenue apartment. In November 2014, the pocket watch sold for a record price of 24 million dollars at auction. Graves initially paid 60,000 CHF when he commissioned the watch, which is equal to about 200,000 USD today. The Supercomplication is the most complicated watch ever built without computer assistance. In 1989, Patek Philippe celebrated their 150th anniversary and unveiled the Calibre 89 pocket watch, which, with 1,728 individual pieces, is even more complicated than the Supercomplication.

In November 2016, Patek Philippe broke another record: A watch with reference number 1518 sold at auction for 9.6 million Swiss francs. It was the highest price ever paid for a wristwatch. This precious timepiece is a stainless steel chronograph with a perpetual calendar.