(Last updated: May 22, 2019)
Ever since ycruncher was unlocked in 2010 to allow anybody to set a record, it's become somewhat of a competition to stay atop the board. And because of this, some rules need to be set to keep things fair and to ensure an acceptable level of confidence that the computations are correct.
If you wish to set a record, you must:
*The validation files are protected with a checksum to prevent tampering/cheating. People have tried to cheat before  which is why we can't have nice things.
Exceptions for Pi:
Pi is special since it is the constant and everybody pushes to the extreme limit to compute it. Therefore there is a special method to verify Pi that doesn't require a second computation.
Note that for anyone attempting to set a Pi world record: Should the attempt succeed, I kindly ask that you make yourself sufficiently available for external requests to access or download the digits in its entirety (at least until it is broken again by someone else). Pi is popular enough that people do actually want to see the digits.
To compute and verify Pi using only one computation, you must:
#1 and #2 are needed because only the builtin swap mode implementations have the final verification step to ensure that errors are propagated to the last digits.
#3 is needed because you need the hexadecimal digits to compare with the BBP computation.
The rest are selfexplanatory.
The BBP formula computation (#6) is very fast compared to the main computation. If you're attempting a Pi world record and you've been in contact with me the whole time, I will probably be doing this step for you on my own hardware as you near the end of your computation. So I will probably have the hexadecimal digits waiting for you at the end of the main computation.
This BBP formula method can theoretically be extended to other constants as well. But none of them have the additional verification steps to make this valid.
Custom Formulas:
The rule is that in order to claim a world record, you must do the computation using two computationally independent methods. This (unwritten) rule has existed for many decades and has long preceeded ycruncher. Exceptions can be made only if there is an alternate method of verification.
"Computationally independent" means that any errors (hardware or software) that occur in either computation will (with extreme probability) cause the computations to either fail, or have mismatching digits.
For example, the following two methods to compute sqrt(Pi) are dependent:
If there is a bug in the implementation of the square root function, both computations will yield the same (incorrect) results. It doesn't matter if Pi itself is done using different algorithms*.
Up until ycruncher v0.7.6, all the algorithms that it has provided for the same constant are indeed independent. This was intentional so that anybody can pick any two algorithms and run a compute/verify pair  no questions asked. But this changes in ycruncher v0.7.7 due to the custom formula feature. Now you can enter your own formulas. And thus there is no longer any protection against using two formulas that are computationally dependent.
The line between whether a pair of formulas is sufficiently independent is not welldefined. So I will be making a judgement call on these. And I will reject world records done using a pair of formulas if I deem them to be too similar or not computationally independent.
_{*The same argument can be made about ycruncher's radix conversion since all computations and all formulas will go through the same radix conversion code. The "Output Verify" option enables a series of verification steps for both the radix conversion and the output of digits to disk. This ensures that there is no single point of failure (hardware or software) that can lead to incorrect digits being undetected.}
What Constants are Tracked:
Since there's an unlimited number of things that can be computed, I will only track a small subset of them.
The official list is (in approximate order of popularity and mathematical importance):
Constant  First Digits  Current World Record  
Verified  Unverified  
Pi  3.14159265358979323846264338327950288419716939937510...  31,415,926,535,897  
e  2.71828182845904523536028747135266249775724709369995...  8,000,000,000,000  
EulerMascheroni Constant  0.57721566490153286060651209008240243104215933593992...  477,511,832,674  
Sqrt(2)  1.41421356237309504880168872420969807856967187537694...  10,000,000,000,000  
Golden Ratio  1.61803398874989484820458683436563811772030917980576...  3,000,000,000,100  16,180,339,887,498 
Log(2)  0.69314718055994530941723212145817656807550013436025...  1,000,000,000,000  
Zeta(3)  Apery's Constant  1.20205690315959428539973816151144999076498629234049...  500,000,000,000  
Catalan's Constant  0.91596559417721901505460351493238411077414937428167...  500,000,000,000  
Lemniscate  5.24411510858423962092967917978223882736550990286324...  310,000,000,000  600,000,000,000 
Gamma(1/4)  3.62560990822190831193068515586767200299516768288006...  362,560,990,822  
Gamma(1/3)  2.67893853470774763365569294097467764412868937795730...  200,000,000,000  
Log(10)  2.30258509299404568401799145468436420760110148862877...  600,000,000,000  
Zeta(5)  1.03692775514336992633136548645703416805708091950191...  100,000,000,000 
As of this writing, all of these records are currently held by ycruncher. But of course this can and will eventually change in the future.
Blue: Current World Record
Green: Former World Record
Red: Unverified computation.*
*To protect against computation errors from software bugs and/or hardware instability, a computation must be verified before it counts as a world record.
This is usually done by repeating the computation using a different and independent formula.
Date Announced  Date Completed:  Source:  Who:  Constant:  Decimal Digits:  Time:  Computer: 
May 22, 2019  May 21, 2019  Screen  Seungmin Kim 
Lemniscate  600,000,000,000  2 x Intel Xeon Gold 6140 @ 2.3 GHz 187 GB 2 x Intel Xeon 8260L @ 2.4 GHz 768 TB + 6 TB Optane 

May 8, 2019  May 8, 2019  Johannes Kloimböck  Lemniscate  310,000,000,000  Intel Xeon E31230 v6 @ 3.5 GHz 32 GB 

May 8, 2019  May 7, 2019  Seungmin Kim  Lemniscate  600,000,000,000 
Not Verified 
2 x Intel Xeon Gold 6140 @ 2.3 GHz 187 GB 

April 29, 2019  April 26, 2019  Jacob Riffee  Log(2)  1,000,000,000,000  Compute: 30.9 days  Intel Xeon E52660 @ 2.2 GHz 32 GB + 6 x 4 TB HD 

April 22, 2019  April 20, 2019  Ian Cutress  Gamma(1/4)  362,560,990,822  Compute: 3.01 days  
April 15, 2019  April 14, 2019  Ian Cutress  Log(10)  600,000,000,000  2 x Intel Xeon 8170M @ 2.1 GHz 384 GB + 2 x 2 TB SSD 

April 9, 2019  April 7, 2019  Ian Cutress  Log(2)  693,147,180,559  
April 7, 2019  April 7, 2019  Screen  Lucian Ilea  Lemniscate  300,000,000,000  2 x Intel Xeon E52690 v4 @ 2.6 GHz 448 GB 2 x Intel Xeon 8260L @ 2.4 GHz 768 GB + 5.89 TB Optane 

March 29, 2019  March 29, 2019  Screen  Mike A 
Catalan's Constant  500,000,000,000  2 x Intel Xeon E52696 v4 @ 2.2 GHz 768 GB 

March 25, 2019  March 24, 2019  Oliver Kruse 
Zeta(5)  100,000,000,000  AMD Threadripper 1950X @ 3.4 GHz 128 GB 

March 23, 2019  March 17, 2019  Ian Cutress  Zeta(5)  21,000,000,000  Compute: 36.3 hours  
March 14, 2019  January 21, 2019  Blogs 
Emma Haruka Iwao  Pi  31,415,926,535,897  Compute: 121 days  2 x Undisclosed Intel Xeon @ 2.00 GHz > 1.40 TB DDR4 > 240 TB SSD 
March 3, 2019  March 3, 2019  Screen  Alexander Yee  Gamma(1/3)  200,000,000,000  Compute: 42.5 hours  Intel Core i7 5960X @ 4.0 GHz 64 GB  16 x 2TB 7200 RPM 
March 3, 2019  February 26, 2019  Screen  Alexander Yee  Gamma(1/3)  100,000,000,000  Compute: 35.8 hours  Intel Core i7 5960X @ 4.0 GHz 64 GB  16 x 2TB 7200 RPM 
February 23, 2019  February 22, 2019  Screen  Alexander Yee  Gamma(1/3)  20,000,000,000  Compute: 52 minutes  Intel Core i9 7940X @ 3.6 GHz 128 GB DDR4 
February 16, 2019  February 16, 2019  Tizian Hanselmann  Catalan's Constant  300,000,000,000  2 x Intel Xeon X5650 @ 2.67 GHz 240 GB 

January 23, 2019  January 23, 2019  Oliver Kruse  Zeta(5)  100,000,000,000 
Verified by Ian Cutress 
AMD Threadripper 1950X @ 3.4 GHz 128 GB 

January 21, 2019  January 17, 2019  Gerald Hofmann  Golden Ratio  16,180,339,887,498 
Not Verified 
2 x AMD Epyc 7551 @ 2.0 GHz 200 GB 

January 6, 2019  January 6, 2019  Tizian Hanselmann  Golden Ratio  3,000,000,000,100  Intel Xeon X5650 @ 2.67 GHz 240 GB 

January 3, 2019  January 3, 2019  Gerald Hofmann  e  8,000,000,000,000  Compute: 28.5 days  2 x AMD Epyc 7551 @ 2.0 GHz 256 GB 

December 10, 2018  December 10, 2018  Michael Kwok  Log(2)  600,000,000,000  Core i7 7700k @ 4.2 GHz  16 GB Core i7 4790 @ 3.6 GHz  16 GB 

November 30, 2018  November 30, 2018  Screen  Alexander Yee  Gamma(1/4)  100,000,000,000  Compute: 32.0 hours  Intel Core i7 5960X @ 4.0 GHz 64 GB  16 x 2TB 7200 RPM 
November 30, 2018  November 27, 2018  Kevin Humphreys  Golden Ratio  3,000,000,000,000  Compute: 10.3 days  Intel Xeon E52640 v2 @ 2.0 GHz 48 GB 

October 29, 2018  October 29, 2018  Screen  Alexander Yee  Gamma(1/4)  50,000,000,000  Compute: 15.5 hours  Intel Core i7 5960X @ 4.0 GHz 64 GB  16 x 2TB 7200 RPM 
October 27, 2018  October 27, 2018  Screen  Alexander Yee  Gamma(1/4)  20,000,000,000  Compute: 60.4 minutes  Intel Core i9 7940X @ 3.6 GHz 128 GB DDR4 
October 6, 2018  October 6, 2018  Screen  Alexander Yee  Zeta(5)  20,000,000,000  Compute: 25.3 hours  Intel Core i9 7940X @ 3.6 GHz 128 GB DDR4 
September 23, 2018  September 23, 2018  Tizian Hanselmann  Golden Ratio  2,600,000,000,000  Compute: 9.25 days  2 x Intel Xeon E5620 @ 2.4 GHz 

August 28, 2018  August 28, 2018  "yoyo" & Ryan Moore 
Golden Ratio  2,500,000,000,000  Compute: 42.2 hours  2 x Intel Xeon E52696 v4 @ 2.2 GHz Intel Core i7 7700K @ 4.2 GHz 32 GB 

August 24, 2017  August 23, 2017  Ron Watkins  EulerMascheroni Constant  477,511,832,674  4 x Xeon E54660 v3 @ 2.1 GHz  1 TB 2 x Xeon X5690 @ 3.47 GHz  128 GB 

August 14, 2017  August 13, 2017  Ron Watkins  Zeta(3)  Apery's Constant  500,000,000,000  8 x Xeon 6550 @ 2.0 GHz  512 GB 2 x Xeon X5690 @ 3.46 GHz  142 GB 

November 15, 2016  November 11, 2016  Blog Sponsor 
Peter Trueb  Pi  22,459,157,718,361  Compute: 105 days  4 x Xeon E78890 v3 @ 2.50 GHz 1.25 TB DDR4 20 x 6 TB 7200 RPM Seagate 
September 3, 2016  August 29, 2016  Ron Watkins  e  5,000,000,000,000  2 x Xeon X5690 @ 3.47 GHz 141 GB 

July 11, 2016  July 5, 2016  "yoyo"  Golden Ratio  10,000,000,000,000 
Not Verified 
2 x Intel Xeon E52696 v4 @ 2.2 GHz 768 GB 

June 28, 2016  June 19, 2016  Ron Watkins  Square Root of 2  10,000,000,000,000  2 x Xeon X5690 @ 3.47 GHz 141 GB 

June 4, 2016  May 29, 2016  Ron Watkins  Lemniscate  250,000,000,000  4 x Xeon E54660 v3 @ 2.1 GHz  1TB 4 x Xeon X6550 @ 2 GHz  512 GB 

June 4, 2016  May 29, 2016  "yoyo"  e  2,500,000,000,000 
Not Verified 
2 x Intel Xeon E52696 v4 @ 2.2 GHz 768 GB 

June 4, 2016  June 2, 2016  "yoyo"  Golden Ratio  5,000,000,000,000 
Not Verified 
2 x Intel Xeon E52696 v4 @ 2.2 GHz 768 GB 

May 25, 2016  May 18, 2016  Ron Watkins  EulerMascheroni Constant  250,000,000,000  2 x Xeon E54660 v3 @ 2.1 GHz  1 TB 4 x Xeon X6550 @ 2.0 GHz  512 GB 

April 28, 2016  April 28, 2016  "yoyo"  Golden Ratio  2,500,000,000,000 
Verified by Ryan Moore 
2 x Intel Xeon E52696 v4 @ 2.2 GHz 768 GB 

April 24, 2016  April 18, 2016  Ron Watkins  Log(2)  500,000,000,000  4 x Xeon X5690 @ 3.47 GHz  141 GB  
April 17, 2016  April 12, 2016  Ron Watkins  Catalan's Constant  250,000,000,000  4 x Xeon E54660 v3 @ 2.1 GHz 1 TB 

April 9, 2016  April 3, 2016  Ron Watkins  Lemniscate  200,000,000,000  4 x Xeon X6550 @ 2 GHz  492 GB  
April 9, 2016  April 3, 2016  Ron Watkins  Log(10)  500,000,000,000  2 x Xeon X5690 @ 3.47 GHz 141 GB 

April 3, 2016  April 2, 2016  Ron Watkins  Square Root of 2  5,000,000,000,000  4 x Xeon X7350 @ 2.93 GHz 96 GB 

March 16, 2016  March 15, 2016  Peter Trueb  EulerMascheroni Constant  160,000,000,000  4 x Xeon E78890 v3 @ 2.5 GHz 1.25 TB 

February 9, 2016  Peter Trueb  Lemniscate  190,000,000,000  4 x Xeon E78890 v3 @ 2.5 GHz 1.25 TB 

February 17, 2016  February 14, 2016  Ron Watkins  e  1,500,000,000,000  2 x Xeon X5690 @ 3.47 GHz 141 GB 

February 8, 2016  February 7, 2016  Ron Watkins  Log(10)  250,000,000,000  4 x Xeon X6550 @ 2 GHz  512 GB  
February 8, 2016  Johan Lundqvist  Log(10)  240,000,000,000 
Not Verified 
2 x Intel Xeon E52698 v3 @ 2.3 GHz 204 GB 

February 6, 2016  Mike A  Catalan's Constant  500,000,000,000 
Verified by Ian Cutress 
2 x Intel Xeon E52697 v3 @ 2.6 GHz 128 GB 

February 1, 2016  January 30, 2016  Ron Watkins  Log(2)  350,000,000,000  4 x Xeon X6550 @ 2 GHz  512 GB  
January 23, 2016  January 18, 2016  Ben Hadad  Log(10)  211,111,111,111 
Not Verified 
Intel Core i7 5960X @ 3 GHz 32 GB 

January 20, 2016  January 14, 2016  Ron Watkins  Square Root of 2  2,000,000,000,100  2 x Xeon X5690 @ 3.47 GHz 128 GB 

December 21, 2015  December 21, 2015  Dipanjan Nag  Zeta(3)  Apery's Constant  400,000,000,000  Xeon E52698B @ 2.0 GHz  224 GB  
December 21, 2015  December 21, 2015  Ron Watkins  Lemniscate  130,000,000,000  4 x Xeon X6550 @ 2 GHz  492 GB  
November 26, 2015  August 1, 2014  David Hickox  Log(2)  300,000,000,000 
Not Verified 
Intel Core i7 4770K @ 3.5 GHz 16 GB DDR3 

November 22, 2015  November 14, 2015  Ron Watkins  Lemniscate  125,000,000,000  4 x Xeon X6550 @ 2 GHz  256 GB  
October 12, 2015  October 12, 2015  Ethan Gallagher  Lemniscate  120,000,000,000 
Verified by Ron Watkins 
Intel Core i5 4300U @ 2.5 GHz  8 GB  
August 11, 2015  August 7, 2015  Ron Watkins  Zeta(3)  Apery's Constant  250,000,000,000  4 x Xeon X6550 @ 2 GHz  512 GB  
July 24, 2015  July 22, 2015 July 23, 2015 
Source  Ron Watkins Dustin Kirkland 
Golden Ratio  2,000,000,000,000  4 x Xeon X6550 @ 2 GHz  512 GB Xeon E52676 v3 @ 2.4 GHz  64 GB 

July 13, 2015  July 12, 2015  Ron Watkins  Log(2)  250,000,000,000  4 x Xeon X6550 @ 2 GHz  512 GB  
July 8, 2015  July 5, 2015  Ron Watkins  Lemniscate  100,000,000,000  4 x Xeon X6550 @ 2 GHz  512 GB  
June 26, 2015  June, 24, 2015  Ellie Hebert  e  1,400,000,000,000  FX8370 @ 4.0 GHz  8 GB FX8370 @ 4.0 GHz  16 GB 

June 13, 2015  June 13, 2015  Andreas Stiller  Lemniscate  80,000,000,000  4 x Intel Xeon E78890v3 @ 2.5 GHz 512 GB 

June 8, 2015  June 7, 2015  Setti Financial LLC  Catalan's Constant  200,000,001,100 

Intel Core i7 4820K @ 4.5 GHz 24 GB DDR3 

April 1, 2015  April 12, 2015  Ben Hadad  Lemniscate  55,000,000,000  2 x Xeon E52670 v2 @ 2.5 GHz (32 vCPU only)  244 GB Intel Core i7 4790K  8 GB 

March 21, 2015  March 19, 2015  Andreas Stiller  Lemniscate  40,000,000,000  4 x Xeon E74890 v2 @ 2.8 GHz 256 GB DDR3 

February 9, 2015  February 9, 2015  Randy Ready  Lemniscate  15,000,000,000  Amazon Web Services 2 x Xeon E52670 v2 @ 2.5 GHz (32 Logical Cores only) 240 GB DDR3 

October 8, 2014  October 7, 2014  Sandon Van Ness "houkouonchi" 
Pi  13,300,000,000,000  2 x Xeon E54650L @ 2.6 GHz 192 GB DDR3 @ 1333 MHz 24 x 4 TB + 30 x 3 TB 

March 24, 2014  March 10, 2014  Shigeru Kondo  Log(10)  200,000,000,050 

2 x Xeon E52690 @ 3.3 GHz 256 GB DDR3 @ 1600 MHz 12 x 3 TB 

February 28, 2014  Shigeru Kondo  Log(2)  200,000,000,050 

2 x Xeon E52690 @ 3.3 GHz 256 GB DDR3 @ 1600 MHz 12 x 3 TB 

December 28, 2013  December 28, 2013  Source  Shigeru Kondo  Pi  12,100,000,000,050  2 x Xeon E52690 @ 2.9 GHz 128 GB DDR3 @ 1600 MHz 24 x 3 TB 

December 22, 2013  December 22, 2013  Alexander Yee  EulerMascheroni Constant  119,377,958,182 

"Nagisa" 2 x Intel Xeon X5482 @ 3.2 GHz 64 GB DDR2 FBDIMM 64 GB SSD (Boot) + 2 TB (Data) 8 x 2 TB (Computation) 

September 13, 2013  September 13, 2013  Source  Setti Financial LLC  Zeta(3)  Apery's Constant  200,000,001,000  Compute: ~5 months Not Verified 
Intel Core i53570S @ 3.1 GHz 16 GB 
April 8, 2013  April 8, 2013  Source  Setti Financial LLC  Catalan's Constant  100,000,000,000  Compute: ~4 months Not Verified 
2 x Intel Xeon X5460 @ 3.16 GHz 16 GB DDR2 
February 9, 2012  February 9, 2012  Alexander Yee  Square Root of 2  2,000,000,000,050  2 x Xeon X5482 @ 3.2 GHz  64 GB 8 x 2 TB Core i7 2600K @ 4.4 GHz  16 GB 5 x 1 TB + 5 x 2 TB 

October 17, 2011  October 16, 2011  Source  Shigeru Kondo  Pi  10,000,000,000,050  2 x Intel Xeon X5680 @ 3.33 GHz 96 GB DDR3 @ 1066 MHz 24 x 2 TB 

May 24, 2011  May 20, 2011  Shigeru Kondo  Log(10)  100,000,000,000  Compute and Verify: 
Intel Core i7 2500K @ 4.8 GHz 16 GB DDR3 + 6 x 1 TB 

May 14, 2011  Shigeru Kondo  Log(2)  100,000,000,000  Compute and Verify: 
Intel Core i7 2500K @ 4.8 GHz 16 GB DDR3 + 6 x 1 TB 

December 13, 2010  December 12, 2010  Alex Roberts  Catalan's Constant  50,000,000,000  Compute: 35.5 days Not Verified 
AMD Phenom II X4 945 @ 3.0 GHz 8 GB 

December 4, 2010  November 26, 2010  Alex Roberts  Log(2)  50,000,000,000  Compute: 13.1 days Independently Verified 
Intel Core i7 720Q @ 1.60 GHz 4 GB DDR3 

September 17, 2010  September 17, 2010  Source  Alexander Yee  Zeta(3)  Apery's Constant  100,000,001,000  "Nagisa" + "Ushio"  
August 2, 2010  August 2, 2010  Source  Shigeru Kondo & Alexander Yee* 
Pi  5,000,000,000,000  2 x Intel Xeon X5680 @ 3.33 GHz 96 GB DDR3 @ 1066 MHz 16 x 2 TB 

July 8, 2010  July 8, 2010  Source  Alexander Yee  Golden Ratio  1,000,000,000,000 
*Not a continuous run. 
"Nagisa" 2 x Intel Xeon X5482 @ 3.2 GHz 64 GB DDR2 FBDIMM 1.5 TB (Boot + Output) 4 x 1 TB (2 x 2 RAID0) + 6 x 2 TB 
July 5, 2010  July 5, 2010  Source  Shigeru Kondo  e  1,000,000,000,000  Intel Core i7 980X @ 3.33 GHz 12 GB DDR3 2 TB (Boot + Output) 8 x 1 TB (Computation) 

March 22, 2010  March 22, 2010  Source  Shigeru Kondo  Square Root of 2  1,000,000,000,000  Core i7 975 @ 4 GHz  12GB 8 x 1 TB HDs 2 x Xeon W5590  144GB 16 x 2 TB HDs 

February 21, 2010  February 20, 2010  Source  Alexander Yee  e  500,000,000,000  Compute and Verify: 
"Ushio" 
April 16, 2009  April 16, 2009  Source  Alexander Yee & Raymond Chan 
Catalan's Constant  31,026,000,000  Compute: 178 hours Verify: 221 hours 
"Nagisa" 
March 13, 2009  March 13, 2009  Source  Alexander Yee & Raymond Chan 
EulerMascheroni Constant  29,844,489,545  Compute: 205 hours Verify: 269 hours 
"Nagisa" 
February 28, 2009  Source  Alexander Yee & Raymond Chan 
Log(10)  31,026,000,000  Compute and Verify: 
"Nagisa"  
February 15, 2009  Source  Alexander Yee & Raymond Chan 
Zeta(3)  Apery's Constant  31,026,000,000  Compute: 45 hours Verify: 44 hours 
"Nagisa"  
February 4, 2009  Source  Alexander Yee & Raymond Chan 
Log(2)  31,026,000,000  Compute: 24 hours Verify: 16 hours 
"Nagisa"  
January 31, 2009  January 31, 2009  Source  Alexander Yee & Raymond Chan 
Catalan's Constant  15,510,000,000  Compute: 88 hours Verify: 100 hours 
"Nagisa" 
January 21, 2009  January 21, 2009  Source  Alexander Yee & Raymond Chan 
Zeta(3)  Apery's Constant  15,510,000,000  Compute: 20 hours Verify: 21 hours 
"Nagisa" 
January 18, 2009  January 18, 2009  Source  Alexander Yee & Raymond Chan 
EulerMascheroni Constant  14,922,244,771  Compute: 96 hours Verify: 134 hours 
"Nagisa" 
January 7, 2009  Source  Alexander Yee & Raymond Chan 
Log(2)  15,500,000,000  Compute: 12.5 hours Verify: 8.3 hours 
"Nagisa" 
*This first world record for Pi was run entirely by Shigeru Kondo, but with a lot of support from me (Alexander Yee) to get it done. There was also a lot of backandforth testing between the two of us to stabilize the ycruncher software before he could actually run the main computation.
After this first record, we had more or less learned what was needed. So from there on, all the later records were mostly on his own.
This is a list of other notably large computations. They are notable either because they are long running and either came close to a record, or are for less popular constants that nobody tracks.
In order to keep this table from getting out of hand, starting October 19, 2018, I will only officially be tracking world records for:
Everything else will be on a casebycase basis. And I won't be accepting anything new unless it is a very expensive computation which I'll handwavingly define as:
Blue: Current World Record
Green: Former world record or not a world record.
Red: Unverified computation or not a world record.
Date Announced  Date Completed:  Source:  Who:  Constant:  Decimal Digits:  Time:  Computer: 
May 21, 2019  May 9, 2019  Screen  newalex  Pi  2,500,000,000,000  Compute: 5.49 days  2 x Intel Xeon E52686 v4 @ 2.3 GHz 
April 29, 2019  April 28, 2019  Shivam N Patel  Log(7)  105,000,000,000  Compute: 30.3 days
Not Verified 
2 x Intel Xeon E52620 v4 @ 2.1 GHz 128 GB 

April 29, 2019  April 22, 2019  newalex  Gamma(1/4)  250,000,000,000  2 x Intel Platinum 8175M @ 2.5 GHz 756 GB 

April 29, 2019  April 9, 2019  Johannes Kloimböck  Sin(1)  150,000,000,000  Intel Core i5 6200U @ 2.3 GHz 4 GB 

January 6, 2019  December 8, 2018  Tizian Hanselmann  Sqrt(11)  1,000,000,000,000  Intel Xeon X5650 @ 2.67 GHz 240 GB 

December 23, 2018  December 19, 2018  Johannes Kloimböck  Log(5)  120,000,000,000  Intel Xeon E31230 v2 @ 3.3 GHz 8 GB 

November 26, 2018  November 23, 2018  Hsing Lo  Sqrt(11)  500,000,000,000  Intel Core i5 6198DU @ 2.4 GHz 4 GB 

July 23, 2018  July 16, 2018  Tizian Hanselmann  Sqrt(11)  300,000,000,000  Intel Xeon X5650 @ 2.67 GHz 240 GB 

October 30, 2018  October 30, 2018  Screen  Alexander Yee  Cos(1)  250,000,000,000  Intel Core i7 5960X @ 4.0 GHz 64 GB  16 x 2TB 7200 RPM 

October 27, 2018  October 27, 2018  Screen  Alexander Yee  Log(5)  100,000,000,000  Intel Core i7 5960X @ 4.0 GHz 64 GB  16 x 2TB 7200 RPM 

October 27, 2018  October 26, 2018  Screen  Alexander Yee  Log(7)  100,000,000,000  Intel Core i7 5960X @ 4.0 GHz 64 GB  16 x 2TB 7200 RPM 

October 27, 2018  October 14, 2018  Alexander Yee  Sin(1)  100,000,000,000  Intel Core i7 5960X @ 4.0 GHz 64 GB  16 x 2TB 7200 RPM 

October 27, 2018  October 26, 2018  Johannes Kloimböck  Log(5)  5,000,000,000  Intel Xeon E31230 v2 @ 3.3 GHz 4 GB 

October 27, 2018  October 26, 2018  Hsing Lo  Log(5)  2,000,000,000  Intel Core i5 6198U @ 2.4 GHz 4 GB 

October 25, 2018  October 25, 2018  Pablo Barros  Log(7)  20,000,000,000  2 x Intel Xeon E52687 @ 3.1 GHz 128 GB 

October 25, 2018  October 24, 2018  Hsing Lo  Log(7)  5,000,000,000  Intel Core i5 6198U @ 2.4 GHz 4 GB 

October 25, 2018  October 20, 2018  Johannes Kloimböck  Log(7)  5,000,000,000  Intel Core i5 6200U @ 2.4 GHz 4 GB 

October 19, 2018  October 18, 2018  Jacob Riffee  Log(7)  2,500,000,000  Intel Core i7770HQ @ 2.8 GHz 16 GB 

October 10, 2018  September 26, 2018  Jiahao He (狼正ヒロシ)  Log(7)  1,000,000,000  Intel Core i5 6200U @ 2.4 GHz 12 GB 

July 23, 2018  July 16, 2018  Tizian Hanselmann  Sqrt(11)  200,000,000,000  Intel Xeon E5620 @ 2.4 GHz 64 GB 

September 19, 2016  September 12, 2016  David Galilei Natale  Sqrt(5)  1,700,000,000,000  Intel Core i7 3970X @ 3.2 GHz 64 GB 

July 17, 2016  July 12, 2016  David Galilei Natele  e  1,600,000,000,000  Intel Core i7 3970X @ 3.2 GHz  
June 28, 2016  June 12, 2016  David Galilei Natele  e  1,280,000,000,000  Intel Core i7 3970X @ 3.2 GHz  
June 4, 2016  May 17, 2016  "yoyo"  ArcCoth(2)  100,000,000,000  2 x Intel Xeon E52696 v4 @ 2.2 GHz 768 GB 

May 18, 2016  April 30, 2016  David Hickox  Log(10)  350,000,000,000  Intel Core i7 4770K @ 3.5 GHz 16 GB DDR3 

May 18, 2016  May 14, 2016  Ethan Gallagher  Sqrt(11)  100,000,000,000  Intel Core i5 4300U @ 2.5 GHz 8 GB 

April 9, 2016  March 26, 2016  Ron Watkins  Sqrt(5)  1,000,000,000,000  2 x Xeon X5690 @ 3.47 GHz  141 GB 2 x Xeon E5450 @ 3.0 GHz  16 GB 

April 3, 2016  March 27, 2016  Ron Watkins  Sqrt(7)  1,000,000,000,000  2 x Xeon X5690 @ 3.47 GHz 141 GB 

March 22, 2016  Ron Watkins  Sqrt(3)  1,000,000,000,000  2 x Xeon X5690 @ 3.47 GHz 141 GB 

March 21, 2016  March 19, 2016  Dario Ostuni  Sqrt(11)  60,000,000,000  Intel Core i3 2130 @ 3.4 GHz 8 GB 

February 8, 2016  February 6, 2016  Ethan Gallagher  Sqrt(5)  150,000,000,000  Intel Core i5 4300U @ 2.5 GHz 8 GB 

February 1, 2016  January 30, 2016  Ron Watkins  Sqrt(3)  600,000,000,000  2 x Xeon E5450 @ 3.0 GHz 16 GB 

January 30, 2016  Ethan Gallagher  Sqrt(5)  100,000,000,000  Intel Core i5 4300U @ 2.5 GHz 8 GB 

January 26, 2016  January 25, 2016  Ron Watkins  Sqrt(3)  125,000,000,000  2 x Xeon E5450 @ 3.0 GHz 16 GB 

January 24, 2016  Ben Hadad  Sqrt(5)  85,000,000,000  Intel Core i7 5960X @ 3.0 GHz 32 GB 

January 23, 2016  Ben Hadad  Sqrt(3)  350,000,000,000  Intel Core i7 5960X @ 3.0 GHz 32 GB 

February 4, 2016  January 23, 2016  Ethan Gallagher  Sqrt(3)  150,000,000,001  Intel Core i5 4300U @ 2.5 GHz 8 GB 

January 20, 2016  January 14, 2016  Ethan Gallagher  Sqrt(3)  100,000,000,000  Intel Core i5 4300U @ 2.5 GHz 8 GB 

January 11, 2016  January 7, 2016  Ron Watkins  Sqrt(3)  91,804,925,913  4 x Xeon X6550 @ 2 GHz  504 GB  
December 27, 2015  December 24, 2015  Ethan Gallagher  Sqrt(11)  50,000,000,000  Intel Core i5 4300U @ 2.5 GHz 8 GB 

December 24, 2015  Ethan Gallagher  Sqrt(7)  50,000,000,000  Intel Core i5 4300U @ 2.5 GHz 8 GB 

December 24, 2015  Ethan Gallagher  Sqrt(5)  50,000,000,000  Intel Core i5 4300U @ 2.5 GHz 8 GB 

December 23, 2015  Ethan Gallagher  Sqrt(3)  50,000,000,000  Intel Core i5 4300U @ 2.5 GHz 8 GB 

June 4, 2016  October 23, 2016  Timothy J Flynn  ArcCoth(2)  2,000,000,000  2 x Intel Xeon X5460 @ 3.16 GHz 8 GB 

March 29, 2015  March 28, 2015  Ben Hadad  Lemniscate  30,000,000,000  Intel Core i7 4790K @ 4.0 GHz 8 GB DDR3 

March 29, 2015  March 18, 2014  David Hickox  Log(3)  200,000,000,000  Intel Core i7 4770K @ 3.5 GHz 16 GB DDR3 