Pi calculated to massive 2.7 trillion digits

French scientist says Linux-based computer took 131 days to do calculation

A French scientist says he has calculated pi out to an unreal 2.7 trillion digits - a feat that took his Linux-based PC 131 days to calculate. 

The new pi number calculated by software engineer Fabric Ballard would take up more than a terabyte of hard disk space - enough to hold 1,000 copies of the Encyclopedia Britannica and reciting one number per second would take more than 85,000 years, according to this site

Pi you may or may not recall is the ratio of a circle's circumference to its diameter and is approximately equal to 3.14159 and well beyond. 

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The new number is some 123 billion more than the previous record held by Daisuke Taka-hashi at the University of Japan who emplyed a T2K Open Supercomputer. 

According to Bellard's Web site, the following number of digits was computed:

  • 2242301460000 hexadecimal digits (base 16)
  • 2699999990000 decimal digits (base 10

Bellard states that all the software used in the computation was written by him. The most important part is an arbitrary-precision arithmetic library able to manipulate huge numbers stored on hard disks, he stated. 

If you want the real techie details, have a gander here

Bellard goes on to say he is not especially interested in the digits of Pi, "but in the various algorithms involved to do arbitrary-precision arithmetic." 

He says optimizing these algorithms to get good performance is a difficult programming challenge.  "Arbitrary-precision arithmetic with huge numbers has little practical use, but some of the involved algorithms are interesting to do other things." In particular: 

  • The Discrete Fourier Transform. This transform is widely used in many algorithms and most modern electronic appliances (such as digital televisions, cell phones and music players) include at least one instance of it.
  • The reliable managing of a very large amount of disk storage, at least for a single computer. Specific methods were developed to ensure high reliability and high disk I/O bandwidth. The same ideas can be applied to other fields such as video streaming or data base access.
  • The whole computation is an extensive test for a computer including its CPU, RAM, disk storage and cooling system. A single bit error during the computation gives a bad result. Bad cooling results in a hardware failure. 

Discovering new, large numbers has been a hot button recently. In September a group of such researchers said they, through a technique for multiplying large numbers, figured out congruent numbers up to a trillion. Apparently no one had taken them beyond a billion for some reason. 

 In case you were wondering, the first few congruent numbers are 5, 6, 7, 13, 14, 15, 20, and 21. Many congruent numbers were known prior to the new research. For example, every number in the sequence 5, 13, 21, 29, 37, ..., is a congruent number. But other similar looking sequences, like 3, 11, 19, 27, 35, ...., are more mysterious and each number has to be checked individually.  The calculation found 3,148,379,694 of these more mysterious congruent numbers up to a trillion, the researchers said in a statement. 

Then on October, a 12 million digit prime number, the largest such number ever discovered, landed a voluntary math research group a $100,000 prize from the Electronic Frontier Foundation (EFF).

The number known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1 . A Mersenne number is a positive integer that is one less than a power of two, the group stated. 

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