In number theory, a Leyland number is a number of the form
where x and y are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are
The requirement that x and y both be greater than 1 is important, since without it every positive integer would be a Leyland number of the form x1 + 1x. Also, because of the commutative property of addition, the condition x ≥ y is usually added to avoid double-covering the set of Leyland numbers (so we have 1 < y ≤ x).
One can also fix the value of y and consider the sequence of x values that gives Leyland primes, for example x2 + 2x is prime for x = 3, 9, 15, 21, 33, 2007, 2127, 3759, ... (A064539).
By November 2012, the largest Leyland number that had been proven to be prime was 51226753 + 67535122 with 25050 digits. From January 2011 to April 2011, it was the largest prime whose primality was proved by elliptic curve primality proving. In December 2012, this was improved by proving the primality of the two numbers 311063 + 633110 (5596 digits) and 86562929 + 29298656 (30008 digits), the latter of which surpassed the previous record. There are many larger known probable primes such as 3147389 + 9314738, but it is hard to prove primality of large Leyland numbers. Paul Leyland writes on his website: "More recently still, it was realized that numbers of this form are ideal test cases for general purpose primality proving programs. They have a simple algebraic description but no obvious cyclotomic properties which special purpose algorithms can exploit."
Leyland Numbers and Leyland Primes with Professor Ed Copeland...
Reddit discussion: http://redd.it/2kl1wp
More links & stuff in full description below ↓↓↓
Thanks to Patreon supporters: Herschal Sanders --- Joshua Wilson and Andrew Touchet --- Lê --- Stan Ciprian --- Alex Bozzi --- OK Merli --- Tracy Parry --- Micky Baeza --- plusunim --- Elias Jonathan List --- Filipe Junqueira --- Thomas J. Petersen --- Spiked Math --- Bill Shillito
YOU CAN SUPPORT US TOO: http://www.patreon.com/numberphile
Professor Ed Copeland is a physics and cosmology professor at the University of Nottingham.
With thanks to Paul Leyland: http://www.leyland.vispa.com
The Wikipedia Page is a good jump-off point for plenty of detailed stuff about Leyland Numbers: http://en.wikipedia.org/wiki/Leyland_number
OEIS ...
published: 28 Oct 2014
(NT07) Leyland Numbers
In this video, we introduce a number sequence that is connected to power towers and tetrations, known as Leyland numbers, and describe a few of their properties and how to calculate them.
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LEYLAND VIKING CHASSIS NUMBER & ENGINE NUMBER LOCATION
LEYLAND VIKING CHASSIS NUMBER & ENGINE NUMBER LOCATION.
https://www.facebook.com/caredrive.lk/
http://www.caredrive.lk/
published: 06 Feb 2020
Ashok leyland dost Mini passenger vehicle bus Chassis number location, where is dost chassis number
Ashok leyland dost Mini passenger vehicle bus Chassis number location, where is dost chassis number
#dost #ashokleyland #suzuki #minibus #loader #pickup
published: 05 Oct 2022
Finding a serial number on the engine of a Leyland tractor
When purchasing engine components we ask for the engine serial number so we know what parts to send you. This video shows where to find the serial number on a middleweight Leyland tractor
published: 08 Feb 2019
ASHOK LEYLAND AL 4923 CHASSIS NUMBER LOCATION
ASHOK LEYLAND AL 4923 CHASSIS NUMBER LOCATION
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Chassis number location in Ashok Leyland boss 913
Ashok Leyland boss chassis number location
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ASHOK LEYLAND BS4 CHASSIS NUMBER LOCATION @SARKAR TECH UNIVERSE
Leyland Numbers and Leyland Primes with Professor Ed Copeland...
Reddit discussion: http://redd.it/2kl1wp
More links & stuff in full description below ↓↓↓
Tha...
Leyland Numbers and Leyland Primes with Professor Ed Copeland...
Reddit discussion: http://redd.it/2kl1wp
More links & stuff in full description below ↓↓↓
Thanks to Patreon supporters: Herschal Sanders --- Joshua Wilson and Andrew Touchet --- Lê --- Stan Ciprian --- Alex Bozzi --- OK Merli --- Tracy Parry --- Micky Baeza --- plusunim --- Elias Jonathan List --- Filipe Junqueira --- Thomas J. Petersen --- Spiked Math --- Bill Shillito
YOU CAN SUPPORT US TOO: http://www.patreon.com/numberphile
Professor Ed Copeland is a physics and cosmology professor at the University of Nottingham.
With thanks to Paul Leyland: http://www.leyland.vispa.com
The Wikipedia Page is a good jump-off point for plenty of detailed stuff about Leyland Numbers: http://en.wikipedia.org/wiki/Leyland_number
OEIS Leyland Numbers: http://oeis.org/A076980
Article: http://www.leyland.vispa.com/numth/primes/xyyx.htm
And thanks to the Leyland Brothers for childhood memories! :)
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
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Subscribe: http://bit.ly/Numberphile_Sub
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Videos by Brady Haran
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Leyland Numbers and Leyland Primes with Professor Ed Copeland...
Reddit discussion: http://redd.it/2kl1wp
More links & stuff in full description below ↓↓↓
Thanks to Patreon supporters: Herschal Sanders --- Joshua Wilson and Andrew Touchet --- Lê --- Stan Ciprian --- Alex Bozzi --- OK Merli --- Tracy Parry --- Micky Baeza --- plusunim --- Elias Jonathan List --- Filipe Junqueira --- Thomas J. Petersen --- Spiked Math --- Bill Shillito
YOU CAN SUPPORT US TOO: http://www.patreon.com/numberphile
Professor Ed Copeland is a physics and cosmology professor at the University of Nottingham.
With thanks to Paul Leyland: http://www.leyland.vispa.com
The Wikipedia Page is a good jump-off point for plenty of detailed stuff about Leyland Numbers: http://en.wikipedia.org/wiki/Leyland_number
OEIS Leyland Numbers: http://oeis.org/A076980
Article: http://www.leyland.vispa.com/numth/primes/xyyx.htm
And thanks to the Leyland Brothers for childhood memories! :)
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
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In this video, we introduce a number sequence that is connected to power towers and tetrations, known as Leyland numbers, and describe a few of their properties...
In this video, we introduce a number sequence that is connected to power towers and tetrations, known as Leyland numbers, and describe a few of their properties and how to calculate them.
--The Let's Learn, Nemo Community--*
►YouTube – https://www.youtube.com/LetsLearnNemo
►Facebook – https://www.facebook.com/groups/LetsLearn.Team
►Discord – https://discord.gg/JjdmSma
►Patreon - https://www.patreon.com/LetsLearnNemo
►Website – https://www.LetsLearnNemo.com
#LetsLearnNemo #Mathematics #NumberTheory
In this video, we introduce a number sequence that is connected to power towers and tetrations, known as Leyland numbers, and describe a few of their properties and how to calculate them.
--The Let's Learn, Nemo Community--*
►YouTube – https://www.youtube.com/LetsLearnNemo
►Facebook – https://www.facebook.com/groups/LetsLearn.Team
►Discord – https://discord.gg/JjdmSma
►Patreon - https://www.patreon.com/LetsLearnNemo
►Website – https://www.LetsLearnNemo.com
#LetsLearnNemo #Mathematics #NumberTheory
Ashok leyland dost Mini passenger vehicle bus Chassis number location, where is dost chassis number
#dost #ashokleyland #suzuki #minibus #loader #pickup
Ashok leyland dost Mini passenger vehicle bus Chassis number location, where is dost chassis number
#dost #ashokleyland #suzuki #minibus #loader #pickup
Ashok leyland dost Mini passenger vehicle bus Chassis number location, where is dost chassis number
#dost #ashokleyland #suzuki #minibus #loader #pickup
When purchasing engine components we ask for the engine serial number so we know what parts to send you. This video shows where to find the serial number on a m...
When purchasing engine components we ask for the engine serial number so we know what parts to send you. This video shows where to find the serial number on a middleweight Leyland tractor
When purchasing engine components we ask for the engine serial number so we know what parts to send you. This video shows where to find the serial number on a middleweight Leyland tractor
Leyland Numbers and Leyland Primes with Professor Ed Copeland...
Reddit discussion: http://redd.it/2kl1wp
More links & stuff in full description below ↓↓↓
Thanks to Patreon supporters: Herschal Sanders --- Joshua Wilson and Andrew Touchet --- Lê --- Stan Ciprian --- Alex Bozzi --- OK Merli --- Tracy Parry --- Micky Baeza --- plusunim --- Elias Jonathan List --- Filipe Junqueira --- Thomas J. Petersen --- Spiked Math --- Bill Shillito
YOU CAN SUPPORT US TOO: http://www.patreon.com/numberphile
Professor Ed Copeland is a physics and cosmology professor at the University of Nottingham.
With thanks to Paul Leyland: http://www.leyland.vispa.com
The Wikipedia Page is a good jump-off point for plenty of detailed stuff about Leyland Numbers: http://en.wikipedia.org/wiki/Leyland_number
OEIS Leyland Numbers: http://oeis.org/A076980
Article: http://www.leyland.vispa.com/numth/primes/xyyx.htm
And thanks to the Leyland Brothers for childhood memories! :)
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Other merchandise: https://store.dftba.com/collections/numberphile
In this video, we introduce a number sequence that is connected to power towers and tetrations, known as Leyland numbers, and describe a few of their properties and how to calculate them.
--The Let's Learn, Nemo Community--*
►YouTube – https://www.youtube.com/LetsLearnNemo
►Facebook – https://www.facebook.com/groups/LetsLearn.Team
►Discord – https://discord.gg/JjdmSma
►Patreon - https://www.patreon.com/LetsLearnNemo
►Website – https://www.LetsLearnNemo.com
#LetsLearnNemo #Mathematics #NumberTheory
Ashok leyland dost Mini passenger vehicle bus Chassis number location, where is dost chassis number
#dost #ashokleyland #suzuki #minibus #loader #pickup
When purchasing engine components we ask for the engine serial number so we know what parts to send you. This video shows where to find the serial number on a middleweight Leyland tractor
In number theory, a Leyland number is a number of the form
where x and y are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are
The requirement that x and y both be greater than 1 is important, since without it every positive integer would be a Leyland number of the form x1 + 1x. Also, because of the commutative property of addition, the condition x ≥ y is usually added to avoid double-covering the set of Leyland numbers (so we have 1 < y ≤ x).
One can also fix the value of y and consider the sequence of x values that gives Leyland primes, for example x2 + 2x is prime for x = 3, 9, 15, 21, 33, 2007, 2127, 3759, ... (A064539).
By November 2012, the largest Leyland number that had been proven to be prime was 51226753 + 67535122 with 25050 digits. From January 2011 to April 2011, it was the largest prime whose primality was proved by elliptic curve primality proving. In December 2012, this was improved by proving the primality of the two numbers 311063 + 633110 (5596 digits) and 86562929 + 29298656 (30008 digits), the latter of which surpassed the previous record. There are many larger known probable primes such as 3147389 + 9314738, but it is hard to prove primality of large Leyland numbers. Paul Leyland writes on his website: "More recently still, it was realized that numbers of this form are ideal test cases for general purpose primality proving programs. They have a simple algebraic description but no obvious cyclotomic properties which special purpose algorithms can exploit."
Well, other than former Tigers skipper Jim Leyland. “I think this team, they're gonna get healthy,” Leyland said, on Aug ... When he said that, Leyland was giving a news conference in a small room in the Tigers' press box after his number was retired.
It has captured the faint scent of 2006, when the Tigers came from nowhere in Jim Leyland’s first season as manager to reach the World Series. Leyland was back in Detroit for his number retirement ceremony on Aug.
Hall of Fame manager Jim Leyland on Detroit Tigers retiring his number. Former Detroit Tigers manager Jim Leyland speaks to reporters Tuesday, June 3, 2024, about the team's decision to retire his No ...The Tigers put Leyland's No.
They begin the podcast with stories about former manager Jim Leyland, whose No. 10 became the 10th number ever retired by the Tigers with a pregame ceremony Saturday against the Royals ... Jim Leyland 'always a Tiger'.
Particularly so, on the heels of Saturday night’s stirring extra-inning rally that capped a nostalgic celebration at Comerica Park, where former manager Jim Leyland was honored with a number retirement ceremony.
DETROIT — Jim Leyland's No ... Former Detroit TigersHall of Fame manager Jim Leyland is honored with his number 10 being retired before a baseball game between the Detroit Tigers and Kansas City Royals, Saturday, Aug.
You wanna know what makes Jim Leyland so special?. On the day the Detroit Tigers retired his number, putting his name and No ... “This is the highest honor you could ever get from an individual team to have a team retire your number,” Leyland said.
"They're struggling right this moment and they're not going to get in (to the playoffs)," said Leyland, whose number retirement by the Tigers followed his induction into the Baseball Hall of Fame last month.
DETROIT -- Jim Leyland said he wanted to keep his speech on Saturday short and sweet ... “How can I not love you after all you’ve done for me?” Leyland said ... Tigers retired Leyland’s No.
When. 6.10 p.m. Saturday. Where ... TV ... Radio ... TBD ... The Tigers will also celebrate Jim Leyland's number retirement before Saturday's game ... The first 15,000 fans will receive a "Jim Leyland starter pack," featuring, among other things, a commemorative T-shirt.