Fractran champions: Difference between revisions

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2 fractions; proving n-1 seems very unfun and i'll let someone else prove it
Int-y1 (talk | contribs)
400 edits
m 7 fractions 17 primes isn't proven yet
 
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In this article we focus on the longest running [[Fractran]] programs containing a specific number of fractions and primes.
In this article we focus on the longest running [[Fractran]] programs containing a specific number of fractions and primes.
== Champions with 0 fractions ==
{| class="wikitable"
|+
!Primes used
!Max runtime
!Example champion(s)
!First champion's vector representation
!Champion found
!Notes
|-
|0
|0
|<code>[]</code>
|<math>\begin{bmatrix}\end{bmatrix}</math>
|
|
|}


== Champions with 1 fraction ==
== Champions with 1 fraction ==
Line 18: Line 37:
  -1 \end{bmatrix}</math>
  -1 \end{bmatrix}</math>
|
|
|
|BBf(2)
|-
|-
|2
|2
Line 26: Line 45:
  -1 &  1 \end{bmatrix}</math>
  -1 &  1 \end{bmatrix}</math>
|
|
|
|BBf(3)
|-
|-
|3
|3
Line 34: Line 53:
  -1 &  2 \end{bmatrix}</math>
  -1 &  2 \end{bmatrix}</math>
|
|
|
|BBf(4)
|-
|-
|4
|4
Line 43: Line 62:
|
|
|
|
|-
|...
|-
|-
|n
|n
Line 81: Line 102:
   0 & -1 \end{bmatrix}</math>
   0 & -1 \end{bmatrix}</math>
|
|
|
|BBf(5)
|-
|-
|4
|4
Line 91: Line 112:
   0 & -1 \end{bmatrix}</math>
   0 & -1 \end{bmatrix}</math>
|
|
|
|BBf(6)
|-
|-
|5
|5
Line 101: Line 122:
   0 & -1 \end{bmatrix}</math>
   0 & -1 \end{bmatrix}</math>
|
|
|
|BBf(7)
|-
|-
|6
|6
Line 111: Line 132:
   0 & -1 \end{bmatrix}</math>
   0 & -1 \end{bmatrix}</math>
|
|
|
|BBf(8)
|-
|-
|7
|7
Line 121: Line 142:
   0 & -1 \end{bmatrix}</math>
   0 & -1 \end{bmatrix}</math>
|
|
|
|BBf(9)
|-
|-
|8
|8
Line 131: Line 152:
   0 & -1 \end{bmatrix}</math>
   0 & -1 \end{bmatrix}</math>
|
|
|
|BBf(10)
|-
|-
|9
|9
Line 142: Line 163:
|
|
|
|
|-
|...
|-
|-
|n
|n
|≥n-1
|n-1
|<math>[3^{n-2}/2, 1/3]</math>
|<math>[3^{n-2}/2, 1/3]</math>
<math>[1/3, 3^{n-2}/2]</math>
<math>[1/3, 3^{n-2}/2]</math>
Line 150: Line 173:
  -1 & n-2 \\
  -1 & n-2 \\
   0 & -1 \end{bmatrix}</math>
   0 & -1 \end{bmatrix}</math>
|
|
|}
== Champions with 3 fractions ==
{| class="wikitable"
|+
!Primes used
!Max runtime
!Example champion(s)
!First champion's vector representation
!Champion found
!Notes
|-
|3
|1
|<code>[1/2, 1/2, 1/2]</code>
|<math>\begin{bmatrix}
-1 \\
-1 \\
-1 \end{bmatrix}</math>
|
|
|-
|4
|2
|<pre>[3/2, 1/3, 1/2]
[1/3, 3/2, 1/2]</pre>
|<math>\begin{bmatrix}
-1 &  1 \\
  0 & -1 \\
-1 &  0 \end{bmatrix}</math>
|
|
|-
|5
|3
|<pre>[9/2, 1/3, 1/2]
[3/2, 5/3, 1/5]
[15/2, 1/3, 1/5]</pre>
|<math>\begin{bmatrix}
-1 &  2 \\
  0 & -1 \\
-1 &  0 \end{bmatrix}</math>
|
|
|-
|6
|5
|<code>[9/2, 5/3, 1/5]</code>
|<math>\begin{bmatrix}
-1 &  2 &  0 \\
  0 & -1 &  1 \\
  0 &  0 & -1 \end{bmatrix}</math>
|
|
|-
|7
|7
|<pre>[9/2, 25/3, 1/5]
[27/2, 5/3, 1/5]</pre>
|<math>\begin{bmatrix}
-1 &  2 &  0 \\
  0 & -1 &  2 \\
  0 &  0 & -1 \end{bmatrix}</math>
|
|
|-
|8
|10
|<code>[27/2, 25/3, 1/5]</code>
|<math>\begin{bmatrix}
-1 &  3 &  0 \\
  0 & -1 &  2 \\
  0 &  0 & -1 \end{bmatrix}</math>
|
|BBf(11)
|-
|9
|13
|<pre>[27/2, 125/3, 1/5]
[81/2, 25/3, 1/5]</pre>
|<math>\begin{bmatrix}
-1 &  3 &  0 \\
  0 & -1 &  3 \\
  0 &  0 & -1 \end{bmatrix}</math>
|
|BBf(12)
|-
|10
|17
|<code>[81/2, 125/3, 1/5]</code>
|<math>\begin{bmatrix}
-1 &  4 &  0 \\
  0 & -1 &  3 \\
  0 &  0 & -1 \end{bmatrix}</math>
|
|BBf(13)
|-
|11
|21
|<pre>[81/2, 625/3, 1/5]
[243/2, 125/3, 1/5]</pre>
|<math>\begin{bmatrix}
-1 &  4 &  0 \\
  0 & -1 &  4 \\
  0 &  0 & -1 \end{bmatrix}</math>
|
|BBf(14)
|-
|12
|26
|<code>[243/2, 625/3, 1/5]</code>
|<math>\begin{bmatrix}
-1 &  5 &  0 \\
  0 & -1 &  4 \\
  0 &  0 & -1 \end{bmatrix}</math>
|
|
|-
|...
|-
|2n
|<math>\ge n^2-2n+2</math>
|<math>[3^{n-1}/2, 5^{n-2}/3, 1/5]</math>
|<math>\begin{bmatrix}
-1 & n-1 &  0 \\
  0 &  -1 & n-2 \\
  0 &  0 &  -1 \end{bmatrix}</math>
|
|
|-
|2n+1
|<math>\ge n^2-n+1</math>
|<math>[3^{n-1}/2, 5^{n-1}/3, 1/5]</math>
|<math>\begin{bmatrix}
-1 & n-1 &  0 \\
  0 &  -1 & n-1 \\
  0 &  0 &  -1 \end{bmatrix}</math>
|
|
|}
== Champions with 4 fractions ==
{| class="wikitable"
|+
!Primes used
!Max runtime
!Example champion(s)
!First champion's vector representation
!Champion found
!Notes
|-
|4
|1
|<code>[1/2, 1/2, 1/2, 1/2]</code>
|<math>\begin{bmatrix}
-1 \\
-1 \\
-1 \\
-1 \end{bmatrix}</math>
|
|
|-
|5
|2
|<code>[3/2, 1/3, 1/2, 1/2]</code>
|<math>\begin{bmatrix}
-1 &  1 \\
  0 & -1 \\
-1 &  0 \\
-1 &  0 \end{bmatrix}</math>
|
|
|-
|6
|3
|<pre>[3/2, 5/3, 1/5, 1/2]
[15/2, 1/3, 1/5, 1/2]
[9/2, 1/3, 1/2, 1/2]</pre>
|<math>\begin{bmatrix}
-1 &  1 &  0 \\
  0 & -1 &  1 \\
  0 &  0 & -1 \\
-1 &  0 &  0 \end{bmatrix}</math>
|
|
|-
|7
|5
|<code>[9/2, 5/3, 1/5, 1/2]</code>
|<math>\begin{bmatrix}
-1 &  2 &  0 \\
  0 & -1 &  1 \\
  0 &  0 & -1 \\
-1 &  0 &  0 \end{bmatrix}</math>
|
|
|-
|8
|7
|<pre>[9/2, 25/3, 1/5, 1/2]
[27/2, 5/3, 1/5, 1/2]
[9/2, 5/3, 7/5, 1/7]
[9/2, 35/3, 1/5, 1/7]</pre>
|<math>\begin{bmatrix}
-1 &  2 &  0 \\
  0 & -1 &  2 \\
  0 &  0 & -1 \\
-1 &  0 &  0 \end{bmatrix}</math>
|
|
|-
|9
|11
|<code>[9/2, 25/3, 7/5, 1/7]</code>
|<math>\begin{bmatrix}
-1 &  2 &  0 &  0 \\
  0 & -1 &  2 &  0 \\
  0 &  0 & -1 &  1 \\
  0 &  0 &  0 & -1 \end{bmatrix}</math>
|
|
|-
|10
|16
|<code>[27/2, 25/3, 7/5, 1/7]</code>
|<math>\begin{bmatrix}
-1 &  3 &  0 &  0 \\
  0 & -1 &  2 &  0 \\
  0 &  0 & -1 &  1 \\
  0 &  0 &  0 & -1 \end{bmatrix}</math>
|
|
|-
|11
|28
|<code>[1/45, 4/5, 3/2, 25/3]</code>
|<math>\begin{bmatrix}
  0 & -2 & -1 \\
  2 &  0 & -1 \\
-1 &  1 &  0 \\
  0 & -1 &  2 \end{bmatrix}</math>
|
|BBf(15)
|-
|12
|53
|<code>[1/45, 4/5, 3/2, 125/3]</code>
|<math>\begin{bmatrix}
  0 & -2 & -1 \\
  2 &  0 & -1 \\
-1 &  1 &  0 \\
  0 & -1 &  3 \end{bmatrix}</math>
|
|BBf(16)
|-
|13
|107
|<code>[5/6, 49/2, 3/5, 40/7]</code>
|<math>\begin{bmatrix}
-1 & -1 &  1 &  0 \\
-1 &  0 &  0 &  2 \\
  0 &  1 & -1 &  0 \\
  3 &  0 &  1 & -1 \end{bmatrix}</math>
|
|BBf(17)
|-
|14
|211
|<code>[5/6, 49/2, 3/5, 80/7]</code>
|<math>\begin{bmatrix}
-1 & -1 &  1 &  0 \\
-1 &  0 &  0 &  2 \\
  0 &  1 & -1 &  0 \\
  4 &  0 &  1 & -1 \end{bmatrix}</math>
|
|BBf(18)
|-
|15
|370
|<code>[5/6, 49/2, 3/5, 160/7]</code>
|<math>\begin{bmatrix}
-1 & -1 &  1 &  0 \\
-1 &  0 &  0 &  2 \\
  0 &  1 & -1 &  0 \\
  5 &  0 &  1 & -1 \end{bmatrix}</math>
|
|BBf(19)
|-
|16
|596
|<code>[5/6, 49/2, 3/5, 320/7]</code>
|<math>\begin{bmatrix}
-1 & -1 &  1 &  0 \\
-1 &  0 &  0 &  2 \\
  0 &  1 & -1 &  0 \\
  6 &  0 &  1 & -1 \end{bmatrix}</math>
|
|
|-
|17
|3994
|<code>[7/45, 20/21, 375/2, 9/5]</code>
|<math>\begin{bmatrix}
  0 & -2 & -1 &  1 \\
  2 & -1 &  1 & -1 \\
-1 &  1 &  3 &  0 \\
  0 &  2 & -1 &  0 \end{bmatrix}</math>
|
|
|-
|18
|60133
|<code>[1/45, 80/21, 75/2, 63/5]</code>
|<math>\begin{bmatrix}
  0 & -2 & -1 &  0 \\
  4 & -1 &  1 & -1 \\
-1 &  1 &  2 &  0 \\
  0 &  2 & -1 &  1 \end{bmatrix}</math>
|
|
|-
|19
|270858044796
|<code>[7/45, 4/21, 75/2, 3969/5]</code>
|<math>\begin{bmatrix}
  0 & -2 & -1 &  1 \\
  2 & -1 &  0 & -1 \\
-1 &  1 &  2 &  0 \\
  0 &  4 & -1 &  2 \end{bmatrix}</math>
|
|
|-
|20
|≥270858044796
|<code>[77/45, 4/21, 75/2, 3969/5]</code>
|<math>\begin{bmatrix}
  0 & -2 & -1 &  1 &  1 \\
  2 & -1 &  0 & -1 &  0 \\
-1 &  1 &  2 &  0 &  0 \\
  0 &  4 & -1 &  2 &  0 \end{bmatrix}</math>
|
|Also see 4 fractions 19 primes.
|}
== Champions with 5 fractions ==
{| class="wikitable"
|+
!Primes used
!Max runtime
!Example champion(s)
!First champion's vector representation
!Champion found
!Notes
|-
|5
|1
|<code>[1/2, 1/2, 1/2, 1/2, 1/2]</code>
|
|
|See 4 fractions 4 primes.
|-
|6
|2
|<code>[3/2, 1/2, 1/2, 1/2, 1/2]</code>
|
|
|See 4 fractions 5 primes.
|-
|7
|3
|<code>[3/2, 5/3, 1/5, 1/2, 1/2]</code>
|
|
|See 4 fractions 6 primes.
|-
|8
|5
|<code>[9/2, 5/3, 1/5, 1/2, 1/2]</code>
|
|
|See 4 fractions 7 primes.
|-
|9
|7
|<code>[9/2, 25/3, 1/5, 1/2, 1/2]</code>
|
|
|See 4 fractions 8 primes.
|-
|10
|11
|<code>[9/2, 25/3, 7/5, 1/7, 1/2]</code>
|
|
|See 4 fractions 9 primes.
|-
|11
|16
|<code>[27/2, 25/3, 7/5, 1/7, 1/2]</code>
|
|
|See 4 fractions 10 primes.
|-
|12
|28
|<code>[1/45, 4/5, 3/2, 25/3, 1/2]</code>
|
|
|See 4 fractions 11 primes.
|-
|13
|58
|<code>[5/6, 7/2, 3/5, 40/7, 1/3]</code>
|<math>\begin{bmatrix}
-1 & -1 &  1 &  0 \\
-1 &  0 &  0 &  1 \\
  0 &  1 & -1 &  0 \\
  3 &  0 &  1 & -1 \\
  0 & -1 &  0 &  0 \end{bmatrix}</math>
|
|
|-
|14
|137
|<pre>[9/2, 7/15, 11/3, 5/7, 28/11]
[7/15, 9/2, 11/3, 5/7, 28/11]
[7/15, 11/3, 9/2, 5/7, 28/11]</pre>
|<math>\begin{bmatrix}
-1 &  2 &  0 &  0 &  0 \\
  0 & -1 & -1 &  1 &  0 \\
  0 & -1 &  0 &  0 &  1 \\
  0 &  0 &  1 & -1 &  0 \\
  2 &  0 &  0 &  1 & -1 \end{bmatrix}</math>
|
|
|-
|15
|746
|<pre>[7/15, 22/3, 6/77, 5/2, 9/5]
[7/15, 6/77, 22/3, 5/2, 9/5]
[14/15, 3/77, 10/7, 11/2, 49/11]</pre>
|<math>\begin{bmatrix}
  0 & -1 & -1 &  1 &  0 \\
  1 & -1 &  0 &  0 &  1 \\
  1 &  1 &  0 & -1 & -1 \\
-1 &  0 &  1 &  0 &  0 \\
  0 &  2 & -1 &  0 &  0 \end{bmatrix}</math>
|
|BBf(20)
|-
|16
|31957632
|<pre>[27/10, 5/21, 4/3, 7/2, 9/7]
[7/15, 27/14, 4/3, 5/2, 9/5]
[7/15, 4/3, 27/14, 5/2, 9/5]</pre>
|<math>\begin{bmatrix}
-1 &  3 & -1 &  0 \\
  0 & -1 &  1 & -1 \\
  2 & -1 &  0 &  0 \\
-1 &  0 &  0 &  1 \\
  0 &  2 &  0 & -1 \end{bmatrix}</math>
|
|BBf(21)
|-
|17
|≥7548863488598188537
|<code>[7/30, 27/2, 8/35, 5/3, 7/5]</code>
|<math>\begin{bmatrix}
-1 & -1 & -1 &  1 \\
-1 &  3 &  0 &  0 \\
  3 &  0 & -1 & -1 \\
  0 & -1 &  1 &  0 \\
  0 &  0 & -1 &  1 \end{bmatrix}</math>
|
|Probvious champion. 1 Cryptid remains: [[Fractran#Size_22:_Fenrir|Fenrir]].
|-
|18
|≥113501...261856 (41 digits)
|<pre>[8/15, 9/14, 25/2, 7/25, 10/7]
[9/10, 49/2, 8/21, 5/49, 14/5]
[9/10, 8/21, 49/2, 5/49, 14/5]</pre>
|<math>\begin{bmatrix}
  3 & -1 & -1 &  0 \\
-1 &  2 &  0 & -1 \\
-1 &  0 &  2 &  0 \\
  0 &  0 & -2 &  1 \\
  1 &  0 &  1 & -1 \end{bmatrix}</math>
|
|Probvious champion. 2 Cryptids remain: [[Fractran#Size_22:_Fenrir|Fenrir]] and 1 other Hydra-like Cryptid.
|-
|19
|≥170659...455694 (69 digits)
|<code>[7/30, 27/2, 32/35, 5/3, 7/5]</code>
|<math>\begin{bmatrix}
-1 & -1 & -1 &  1 \\
-1 &  3 &  0 &  0 \\
  5 &  0 & -1 & -1 \\
  0 & -1 &  1 &  0 \\
  0 &  0 & -1 &  1 \end{bmatrix}</math>
|
|
|}
== Champions with 6 fractions ==
{| class="wikitable"
|+
!Primes used
!Max runtime
!Example champion(s)
!First champion's vector representation
!Champion found
!Notes
|-
|15
|149
|<pre>[9/2, 7/15, 11/3, 5/7, 28/11, 1/5]
[7/15, 9/2, 11/3, 5/7, 28/11, 1/5]
[7/15, 11/3, 9/2, 5/7, 28/11, 1/5]</pre>
|<math>\begin{bmatrix}
-1 &  2 &  0 &  0 &  0 \\
  0 & -1 & -1 &  1 &  0 \\
  0 & -1 &  0 &  0 &  1 \\
  0 &  0 &  1 & -1 &  0 \\
  2 &  0 &  0 &  1 & -1 \\
  0 &  0 & -1 &  0 &  0 \end{bmatrix}</math>
|
|
|-
|16
|114613...702295 (63 digits)
|<pre>[1/12, 9/10, 14/3, 11/2, 5/7, 3/11]
[9/10, 1/12, 14/3, 11/2, 5/7, 3/11]</pre>
|<math>\begin{bmatrix}
-2 & -1 &  0 &  0 &  0 \\
-1 &  2 & -1 &  0 &  0 \\
  1 & -1 &  0 &  1 &  0 \\
-1 &  0 &  0 &  0 &  1 \\
  0 &  0 &  1 & -1 &  0 \\
  0 &  1 &  0 &  0 & -1 \end{bmatrix}</math>
|
|Probvious BBf(22) champion.
|-
|17
|≥439325...849183 (125 digits)
|<pre>[10/3, 9/14, 5/4, 121/2, 7/5, 3/11]
[3/4, 25/14, 6/5, 121/2, 7/3, 5/11]
[9/10, 14/3, 7/4, 121/2, 5/7, 3/11]
[9/10, 7/4, 14/3, 121/2, 5/7, 3/11]</pre>
|<math>\begin{bmatrix}
  1 & -1 &  1 &  0 &  0 \\
-1 &  2 &  0 & -1 &  0 \\
-2 &  0 &  1 &  0 &  0 \\
-1 &  0 &  0 &  0 &  2 \\
  0 &  0 & -1 &  1 &  0 \\
  0 &  1 &  0 &  0 & -1 \end{bmatrix}</math>
|
|Assuming AI is correct, probvious BBf(23) champion.
|-
|18
|≥900073...596451 (14449 digits)
|<pre>[14/15, 1/6, 11/3, 441/2, 5/7, 15/11]
[14/15, 1/6, 441/2, 11/3, 5/7, 15/11]</pre>
|<math>\begin{bmatrix}
  1 & -1 & -1 &  1 &  0 \\
-1 & -1 &  0 &  0 &  0 \\
  0 & -1 &  0 &  0 &  1 \\
-1 &  2 &  0 &  2 &  0 \\
  0 &  0 &  1 & -1 &  0 \\
  0 &  1 &  1 &  0 & -1 \end{bmatrix}</math>
|
|Best candidate for BBf(24).
|}
== Champions with 7 fractions ==
{| class="wikitable"
|+
!Primes used
!Max runtime
!Example champion(s)
!First champion's vector representation
!Champion found
!Notes
|-
|16
|? (known to be less than 10000)
|?
|?
|
|
|-
|17
|≥130987...374169 (63 digits)
|<pre>[1/12, 9/10, 14/3, 11/2, 5/7, 3/11, 1/5]
[9/10, 1/12, 14/3, 11/2, 5/7, 3/11, 1/5]</pre>
|<math>\begin{bmatrix}
-2 & -1 &  0 &  0 &  0 \\
-1 &  2 & -1 &  0 &  0 \\
  1 & -1 &  0 &  1 &  0 \\
-1 &  0 &  0 &  0 &  1 \\
  0 &  0 &  1 & -1 &  0 \\
  0 &  1 &  0 &  0 & -1 \\
  0 &  0 & -1 &  0 &  0 \end{bmatrix}</math>
|
|
|
|
|}
|}

Latest revision as of 23:34, 3 October 2026

In this article we focus on the longest running Fractran programs containing a specific number of fractions and primes.

Champions with 0 fractions

Primes used Max runtime Example champion(s) First champion's vector representation Champion found Notes
0 0 [] []

Champions with 1 fraction

Primes used Max runtime Example champion(s) First champion's vector representation Champion found Notes
1 1 [1/2] [−1] BBf(2)
2 1 [3/2] [−11] BBf(3)
3 1 [9/2] [−12] BBf(4)
4 1 [27/2] [−13]
...
n 1 [3n−1/2] [−1n−1]

Champions with 2 fractions

Primes used Max runtime Example champion(s) First champion's vector representation Champion found Notes
2 1 [1/2, 1/2] [−1−1]
3 2 
[3/2, 1/3]
[1/3, 3/2]
 [−110−1] BBf(5)
4 3 
[9/2, 1/3]
[1/3, 9/2]
 [−120−1] BBf(6)
5 4 
[27/2, 1/3]
[1/3, 27/2]
 [−130−1] BBf(7)
6 5 
[81/2, 1/3]
[1/3, 81/2]
 [−140−1] BBf(8)
7 6 
[243/2, 1/3]
[1/3, 243/2]
 [−150−1] BBf(9)
8 7 
[729/2, 1/3]
[1/3, 729/2]
 [−160−1] BBf(10)
9 8 
[2187/2, 1/3]
[1/3, 2187/2]
 [−170−1]
...
n n-1 [3n−2/2,1/3]

[1/3,3n−2/2]

[−1n−20−1]

Champions with 3 fractions

Primes used Max runtime Example champion(s) First champion's vector representation Champion found Notes
3 1 [1/2, 1/2, 1/2] [−1−1−1]
4 2 
[3/2, 1/3, 1/2]
[1/3, 3/2, 1/2]
 [−110−1−10]
5 3 
[9/2, 1/3, 1/2]
[3/2, 5/3, 1/5]
[15/2, 1/3, 1/5]
 [−120−1−10]
6 5 [9/2, 5/3, 1/5] [−1200−1100−1]
7 7 
[9/2, 25/3, 1/5]
[27/2, 5/3, 1/5]
 [−1200−1200−1]
8 10 [27/2, 25/3, 1/5] [−1300−1200−1] BBf(11)
9 13 
[27/2, 125/3, 1/5]
[81/2, 25/3, 1/5]
 [−1300−1300−1] BBf(12)
10 17 [81/2, 125/3, 1/5] [−1400−1300−1] BBf(13)
11 21 
[81/2, 625/3, 1/5]
[243/2, 125/3, 1/5]
 [−1400−1400−1] BBf(14)
12 26 [243/2, 625/3, 1/5] [−1500−1400−1]
...
2n ≥n2−2n+2 [3n−1/2,5n−2/3,1/5] [−1n−100−1n−200−1]
2n+1 ≥n2−n+1 [3n−1/2,5n−1/3,1/5] [−1n−100−1n−100−1]

Champions with 4 fractions

Primes used Max runtime Example champion(s) First champion's vector representation Champion found Notes
4 1 [1/2, 1/2, 1/2, 1/2] [−1−1−1−1]
5 2 [3/2, 1/3, 1/2, 1/2] [−110−1−10−10]
6 3 
[3/2, 5/3, 1/5, 1/2]
[15/2, 1/3, 1/5, 1/2]
[9/2, 1/3, 1/2, 1/2]
 [−1100−1100−1−100]
7 5 [9/2, 5/3, 1/5, 1/2] [−1200−1100−1−100]
8 7 
[9/2, 25/3, 1/5, 1/2]
[27/2, 5/3, 1/5, 1/2]
[9/2, 5/3, 7/5, 1/7]
[9/2, 35/3, 1/5, 1/7]
 [−1200−1200−1−100]
9 11 [9/2, 25/3, 7/5, 1/7] [−12000−12000−11000−1]
10 16 [27/2, 25/3, 7/5, 1/7] [−13000−12000−11000−1]
11 28 [1/45, 4/5, 3/2, 25/3] [0−2−120−1−1100−12] BBf(15)
12 53 [1/45, 4/5, 3/2, 125/3] [0−2−120−1−1100−13] BBf(16)
13 107 [5/6, 49/2, 3/5, 40/7] [−1−110−100201−10301−1] BBf(17)
14 211 [5/6, 49/2, 3/5, 80/7] [−1−110−100201−10401−1] BBf(18)
15 370 [5/6, 49/2, 3/5, 160/7] [−1−110−100201−10501−1] BBf(19)
16 596 [5/6, 49/2, 3/5, 320/7] [−1−110−100201−10601−1]
17 3994 [7/45, 20/21, 375/2, 9/5] [0−2−112−11−1−113002−10]
18 60133 [1/45, 80/21, 75/2, 63/5] [0−2−104−11−1−112002−11]
19 270858044796 [7/45, 4/21, 75/2, 3969/5] [0−2−112−10−1−112004−12]
20 ≥270858044796 [77/45, 4/21, 75/2, 3969/5] [0−2−1112−10−10−1120004−120] Also see 4 fractions 19 primes.

Champions with 5 fractions

Primes used Max runtime Example champion(s) First champion's vector representation Champion found Notes
5 1 [1/2, 1/2, 1/2, 1/2, 1/2] See 4 fractions 4 primes.
6 2 [3/2, 1/2, 1/2, 1/2, 1/2] See 4 fractions 5 primes.
7 3 [3/2, 5/3, 1/5, 1/2, 1/2] See 4 fractions 6 primes.
8 5 [9/2, 5/3, 1/5, 1/2, 1/2] See 4 fractions 7 primes.
9 7 [9/2, 25/3, 1/5, 1/2, 1/2] See 4 fractions 8 primes.
10 11 [9/2, 25/3, 7/5, 1/7, 1/2] See 4 fractions 9 primes.
11 16 [27/2, 25/3, 7/5, 1/7, 1/2] See 4 fractions 10 primes.
12 28 [1/45, 4/5, 3/2, 25/3, 1/2] See 4 fractions 11 primes.
13 58 [5/6, 7/2, 3/5, 40/7, 1/3] [−1−110−100101−10301−10−100]
14 137 
[9/2, 7/15, 11/3, 5/7, 28/11]
[7/15, 9/2, 11/3, 5/7, 28/11]
[7/15, 11/3, 9/2, 5/7, 28/11]
 [−120000−1−1100−1001001−102001−1]
15 746 
[7/15, 22/3, 6/77, 5/2, 9/5]
[7/15, 6/77, 22/3, 5/2, 9/5]
[14/15, 3/77, 10/7, 11/2, 49/11]
 [0−1−1101−1001110−1−1−1010002−100] BBf(20)
16 31957632 
[27/10, 5/21, 4/3, 7/2, 9/7]
[7/15, 27/14, 4/3, 5/2, 9/5]
[7/15, 4/3, 27/14, 5/2, 9/5]
 [−13−100−11−12−100−1001020−1] BBf(21)
17 ≥7548863488598188537 [7/30, 27/2, 8/35, 5/3, 7/5] [−1−1−11−130030−1−10−11000−11] Probvious champion. 1 Cryptid remains: Fenrir.
18 ≥113501...261856 (41 digits) 
[8/15, 9/14, 25/2, 7/25, 10/7]
[9/10, 49/2, 8/21, 5/49, 14/5]
[9/10, 8/21, 49/2, 5/49, 14/5]
 [3−1−10−120−1−102000−21101−1] Probvious champion. 2 Cryptids remain: Fenrir and 1 other Hydra-like Cryptid.
19 ≥170659...455694 (69 digits) [7/30, 27/2, 32/35, 5/3, 7/5] [−1−1−11−130050−1−10−11000−11]

Champions with 6 fractions

Primes used Max runtime Example champion(s) First champion's vector representation Champion found Notes
15 149 
[9/2, 7/15, 11/3, 5/7, 28/11, 1/5]
[7/15, 9/2, 11/3, 5/7, 28/11, 1/5]
[7/15, 11/3, 9/2, 5/7, 28/11, 1/5]
 [−120000−1−1100−1001001−102001−100−100]
16 114613...702295 (63 digits) 
[1/12, 9/10, 14/3, 11/2, 5/7, 3/11]
[9/10, 1/12, 14/3, 11/2, 5/7, 3/11]
 [−2−1000−12−1001−1010−10001001−100100−1] Probvious BBf(22) champion.
17 ≥439325...849183 (125 digits) 
[10/3, 9/14, 5/4, 121/2, 7/5, 3/11]
[3/4, 25/14, 6/5, 121/2, 7/3, 5/11]
[9/10, 14/3, 7/4, 121/2, 5/7, 3/11]
[9/10, 7/4, 14/3, 121/2, 5/7, 3/11]
 [1−1100−120−10−20100−1000200−1100100−1] Assuming AI is correct, probvious BBf(23) champion.
18 ≥900073...596451 (14449 digits) 
[14/15, 1/6, 11/3, 441/2, 5/7, 15/11]
[14/15, 1/6, 441/2, 11/3, 5/7, 15/11]
 [1−1−110−1−10000−1001−12020001−100110−1] Best candidate for BBf(24).

Champions with 7 fractions

Primes used Max runtime Example champion(s) First champion's vector representation Champion found Notes
16 ? (known to be less than 10000) ? ?
17 ≥130987...374169 (63 digits) 
[1/12, 9/10, 14/3, 11/2, 5/7, 3/11, 1/5]
[9/10, 1/12, 14/3, 11/2, 5/7, 3/11, 1/5]
 [−2−1000−12−1001−1010−10001001−100100−100−100]
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