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{{Short description|Software for calculating the bits of Pi}}

'''PiHex''' was a [[distributed computing]] [[project]] to calculate specific [[bits]] of [[Pi]], the greatest calculations of Pi ever successfully attempted. 1,246 contributors used idle time slices on almost two thousand computers to make its calculations. They made use of [[Bellard's formula]] , a faster [[version]] of the [[BBP formula]], with the [[algorithm]] discovered by [[David H. Bailey|Bailey]], [[Peter Borwein|Borwein]], and [[Simon Plouffe|Plouffe]] in [[1995]].

'''PiHex''' was a [[distributed computing]] [[project]] organized by [[Colin Percival]] to calculate specific [[bit]]s of [[pi|{{pi}}]].<ref>{{Cite web|url=http://wayback.cecm.sfu.ca/projects/pihex/index.html|title=PiHex- A distributed effort to calculate Pi|last=Percival|first=Colin|website=wayback.cecm.sfu.ca|access-date=2017-07-09}}</ref> 1,246 contributors<ref>{{Cite web|url=http://wayback.cecm.sfu.ca/projects/pihex/topall.html|title=PiHex's Top Producers|last=Percival|first=Colin|website=wayback.cecm.sfu.ca|access-date=2017-07-09}}</ref> used idle time slices on almost two thousand computers{{Citation needed|date=July 2017}} to make its calculations. The software used for the project made use of [[Bellard's formula]], a faster version of the [[BBP formula]].<ref>{{Cite web|url=http://wayback.cecm.sfu.ca/projects/pihex/about.html|title=About PiHex|last=Percival|first=Colin|website=wayback.cecm.sfu.ca|access-date=2017-07-09}}</ref>

==History==

After setting three records, [[calculating]] 76 [[digits]] past,

To calculate the five trilliontrillionth digit (and the following seventy-six digits) took 13,500 CPU hours, utilizingusing 25 computers from 6 different [[countries]]. FortyThe trillionforty digitstrillionth digit required 84,500 CPU hours and 126 computers from 18 different countries. The highest calculation, the one quadrillionquadrillionth digitsdigit, took 1.2 million computerCPU hours and 1,734 computers from 56 different countries. Total resources: 1,885 computers in 80 unique countries donated 1,298,000.3 million CPU hours. The average computer that was used to calculate would have taken 148 years to complete the calculations alone.{{Citation needed|reason=Unable to find a source for this entire paragraph|date=July 2017}}

in each case ), the five trillionth bit, the forty trillionth bit, and the quadrillionth bit, the project ended September 11, 2000.

After setting three records, calculating the five trillionth bit,<ref name=":0">{{Cite web|url=http://wayback.cecm.sfu.ca/projects/pihex/announce5t.html|title=The five trillionth bit of Pi is '0'|last=Percival|first=Colin|website=wayback.cecm.sfu.ca|access-date=2017-07-09}}</ref> the forty trillionth bit,<ref name=":1">{{Cite web|url=http://wayback.cecm.sfu.ca/projects/pihex/announce40t.html|title=The forty trillionth bit of Pi is '0'|last=Percival|first=Colin|website=wayback.cecm.sfu.ca|access-date=2017-07-09}}</ref> and the quadrillionth bit,<ref name=":2">{{Cite web|url=http://wayback.cecm.sfu.ca/projects/pihex/announce1q.html|title=The quadrillionth bit of Pi is '0'|last=Percival|first=Colin|website=wayback.cecm.sfu.ca|access-date=2017-07-09}}</ref> the project ended on September 11, 2000.<ref>{{Cite web|url=http://wayback.cecm.sfu.ca/projects/pihex/news.html|title=What's New|last=Percival|first=Colin|website=wayback.cecm.sfu.ca|access-date=2017-07-09}}</ref>

[[PiHex]] didn't conduct their task the customary way, using the digits [[0]] through [[9]] ([[Base 10]]). Instead, they calculated Pi in binary (or [[Base 2]], i.e., using only 0s and 1s).

While the PiHex project calculated the least significant digits of {{pi}} ever attempted at the time in any base, the second place is held by Peter Trueb who computed some 22+ trillion digits in 2016 and third place by ''houkouonchi'' who derived the 13.3 trillionth digit in base 10.<ref>{{Cite web|url=http://www.numberworld.org/digits/Pi/|title = Pi}}</ref>

Here were the final [[digit]] strings for each of the three calculations:

==Algorithm==

* Binary digits of Pi from five trillion to five trillion seventy-six (completed [[August 30]], [[1998]]): 001111110010001010111001100111100110001111001000010110101100101111001.

Unlike most computations of {{pi}}, which compute results in [[base 10]], PiHex computed in [[base 2]] (bits), because Bellard's formula and the BBP formula could only be used to compute {{pi}} in base 2 at the time.<ref>{{MathWorld| title=Digit-Extraction Algorithm| urlname=Digit-ExtractionAlgorithm}}</ref>

Here were theThe final [[digit]]bit strings for each of the three calculations resulted as such:

* Binary digits of Pi from forty trillion to forty trillion seventy-six [[(February 9]], [[1999]]): 0000011111001111111110011011100011101000011101011001001111100000.

* Binary digits of Pi{{pi}} from quadrillionfive trillion minus three to quadrillionfive trillion and seventy-six ([[Septembercompleted 11]]August 30, [[2000]]1998):<ref 0011000100001011010110000011010011100101101101100000111010011.name=":0" />

0000 0111 1110 0100 0101 0111 0011 0011 1100 1100

^ Five trillionth bit of {{pi}}

0111 1001 0000 1011 0101 1011 0101 1001 0111 1001

* Binary digits of Pi{{pi}} from forty trillion minus three to forty trillion seventyand sixty-sixfour [[(February 9]], [[1999]]):<ref name=":1" 0000011111001111111110011011100011101000011101011001001111100000./>

1010 0000 1111 1001 1111 1111 0011 0111 0001 1101

^ Forty trillionth bit of {{pi}}

0001 0111 0101 1001 0011 1110 0000

* Binary digits of {{pi}} from one quadrillion minus three to one quadrillion and sixty (September 11, 2000):<ref name=":2" />

1110 0110 0010 0001 0110 1011 0000 0110 1001 1100

^ Quadrillionth bit of {{pi}}

1011 0110 1100 0001 1101 0011

==References==

Therefore, the highest digit of Pi in binary known to man is 1 at position 1,000,000,000,000,076 (one [[quadrillion]] seventy- six) or (10^15)+76.

<references />

[[Category:Pi-related software]]

To calculate five trillion digits took 13,500 CPU hours utilizing 25 computers from 6 different [[countries]]. Forty trillion digits required 84,500 hours and 126 computers from 18 different countries. The highest calculation, one quadrillion digits, took 1.2 million computer hours and 1,734 computers from 56 different countries. Total resources: 1,885 computers in 80 unique countries donated 1,298,000 CPU hours.

[[Category:Distributed computing projects]]

While the PiHex project calculated the highest number of Pi digits ever attemped in any base, second place is held by Professor [[Yasumasa Kanada]] who derived the 1.2411 trillionth digit in Base 10 (which is 5). The popular notion that Kanada calculated Pi to the 1.3511 trillionth digit, and that he found the end of Pi in turn, has not been verified.

{{software-eng-stub}}

==External links==

* [http://oldweb.cecm.sfu.ca/projects/pihex/index.html The official PiHex site]

* [http://www.befria.nu/elias/pi/binpi.html Binary Pi]

* [http://www.befria.nu/elias/pi/lookpi.html A Look at Pi in Binary]

* [http://www.befria.nu/elias/pi/soundpi.html Listen to Pi]

* [http://oldweb.cecm.sfu.ca/projects/pihex/news.html PiHex News]

* [http://oldweb.cecm.sfu.ca/projects/pihex/status.html PiHex Status] {{compu-stub}} {{Category:Distributed computing}}