What function was used for current record of decimal places of EM cnst

In summary, The record for the number of decimal places of accuracy for the Euler-Mascheroni constant stands at 119,377,958,182 decimal places, set by Alexander J. Yee and Raymond Chan in 2009. Yee used the Brent-McMillan algorithm with refinement to achieve this record-breaking result.
  • #1
mesa
Gold Member
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The record for the number of decimal places of accuracy for the Euler-Mascheroni constant stands at just over 29,000,000,000 decimal places set by Alexander J. Yee & Raymond Chan back in 2009. Does anyone know what function they used to set this record?

***EDIT***
On further searching the record now stands at 31,000,000,000 decimal places, Wow!
How do we update wikipedia? :P
***EDIT***
Make that 119,377,958,182 :biggrin:
 
Last edited:
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  • #3
mesa said:
The record for the number of decimal places of accuracy for the Euler-Mascheroni constant stands at just over 29,000,000,000 decimal places set by Alexander J. Yee & Raymond Chan back in 2009. Does anyone know what function they used to set this record?

***EDIT***
On further searching the record now stands at 31,000,000,000 decimal places, Wow!
How do we update wikipedia? :P
***EDIT***
Make that 119,377,958,182 :biggrin:

Took care of it.
 
  • #4
UltrafastPED said:
Formulas are listed here: http://mathworld.wolfram.com/Euler-MascheroniConstant.html

I looked through those before, it seems the fastest converging of the bunch is the one done by Flajolet and Vardi in '96 although I do not understand how the 'n' is used so could be wrong.

SteamKing said:
Took care of it.

And yet another reason why I love PF.
 
  • #6
lurflurf said:
See Alexander J. Yee's site
http://www.numberworld.org/y-cruncher/algorithms.html
He used Brent-McMillan with Refinement.

I was on his site not too long ago, I have no idea how I miss these things...
Thanks for the link, it has exactly what I was asking for!
 

1. What is the significance of the current record of decimal places of EM constant?

The EM constant, also known as the Euler-Mascheroni constant, is a mathematical constant that appears in various areas of mathematics and physics. It is defined as the limiting difference between the harmonic series and the natural logarithm function. The current record of decimal places of EM constant is important for achieving greater precision and accuracy in calculations and for testing the limits of computational algorithms.

2. How is the current record of decimal places of EM constant calculated?

The current record of decimal places of EM constant is calculated using advanced mathematical algorithms and high-performance computing systems. These methods use iterative processes to approximate the value of the constant with increasing accuracy.

3. What is the current record for the number of decimal places of EM constant?

As of 2021, the current record for the number of decimal places of EM constant stands at 50 trillion digits. This record was set by a team of researchers led by Alexander Yee and Shigeru Kondo, using the y-cruncher software on a high-performance computer.

4. Why is it important to continue increasing the accuracy of the current record of decimal places of EM constant?

While the current record of 50 trillion digits is already incredibly precise, it is still an approximation and not the exact value of the constant. As technology and computing power continue to advance, it is important to push the limits of accuracy to gain a deeper understanding of the constant and its applications in different fields of science and mathematics.

5. What are the potential applications of the current record of decimal places of EM constant?

The EM constant has various applications in fields such as number theory, physics, and statistics. It is used to study and solve problems related to the distribution of prime numbers, the behavior of random walks, and the calculation of integrals. The more accurate the value of the constant, the more precise and reliable these applications can be.

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