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Datasets:
cahlen
/
ramanujan-machine-results

Tags:
mathematics
continued-fractions
ramanujan-machine
gpu-computation
number-theory
constant-discovery
License:
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The full dataset viewer is not available (click to read why). Only showing a preview of the rows.
The dataset generation failed
Error code:   DatasetGenerationError
Exception:    ParserError
Message:      Error tokenizing data. C error: EOF inside string starting at row 118
Traceback:    Traceback (most recent call last):
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1872, in _prepare_split_single
                  for key, table in generator:
                                    ^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/csv/csv.py", line 198, in _generate_tables
                  for batch_idx, df in enumerate(csv_file_reader):
                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/pandas/io/parsers/readers.py", line 1843, in __next__
                  return self.get_chunk()
                         ^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/pandas/io/parsers/readers.py", line 1985, in get_chunk
                  return self.read(nrows=size)
                         ^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/pandas/io/parsers/readers.py", line 1923, in read
                  ) = self._engine.read(  # type: ignore[attr-defined]
                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/pandas/io/parsers/c_parser_wrapper.py", line 234, in read
                  chunks = self._reader.read_low_memory(nrows)
                           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "pandas/_libs/parsers.pyx", line 850, in pandas._libs.parsers.TextReader.read_low_memory
                File "pandas/_libs/parsers.pyx", line 905, in pandas._libs.parsers.TextReader._read_rows
                File "pandas/_libs/parsers.pyx", line 874, in pandas._libs.parsers.TextReader._tokenize_rows
                File "pandas/_libs/parsers.pyx", line 891, in pandas._libs.parsers.TextReader._check_tokenize_status
                File "pandas/_libs/parsers.pyx", line 2061, in pandas._libs.parsers.raise_parser_error
              pandas.errors.ParserError: Error tokenizing data. C error: EOF inside string starting at row 118
              
              The above exception was the direct cause of the following exception:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1347, in compute_config_parquet_and_info_response
                  parquet_operations = convert_to_parquet(builder)
                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 980, in convert_to_parquet
                  builder.download_and_prepare(
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 884, in download_and_prepare
                  self._download_and_prepare(
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 947, in _download_and_prepare
                  self._prepare_split(split_generator, **prepare_split_kwargs)
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1739, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                                               ^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1922, in _prepare_split_single
                  raise DatasetGenerationError("An error occurred while generating the dataset") from e
              datasets.exceptions.DatasetGenerationError: An error occurred while generating the dataset

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P_coeffs
string
Q_coeffs
string
value
float64
constant
null
c0
int64
c1
int64
c2
int64
(1,3)
(2,3)
2
null
2
1
-999
(-1,-2)
(-2,-2)
2
null
2
1
-999
(0,-1)
(-2,-2)
2
null
2
1
-999
(3,-1)
(-2,-2)
0.5
null
-4
2
-999
(3,3)
(-2,-3)
2
null
2
1
-999
(1,-3)
(2,-3)
2
null
2
1
-999
(-3,1)
(2,2)
0.5
null
-4
2
-999
(1,2)
(2,2)
2
null
2
1
-999
(2,-2)
(3,-3)
2
null
2
1
-999
(2,-1)
(3,-3)
2
null
2
1
-999
(3,2)
(-2,-2)
2
null
2
1
-999
(0,-3)
(-2,-3)
4
null
4
1
-999
(1,1)
(-2,1)
0.5
null
-4
2
-999
(2,0)
(2,-2)
2
null
2
1
-999
(2,1)
(2,-2)
2
null
2
1
-999
(2,2)
(2,-2)
2
null
2
1
-999
(2,3)
(2,-2)
2
null
2
1
-999
(0,-1)
(-2,-1)
4
null
4
1
-999
(1,1)
(-2,-1)
2
null
2
1
-999
(2,-3)
(-3,3)
2
null
2
1
-999
(2,-2)
(-3,3)
2
null
2
1
-999
(2,-1)
(-3,3)
2
null
2
1
-999
(1,-2)
(-3,1)
4
null
4
1
-999
(3,-2)
(-3,1)
2
null
2
1
-999
(0,-1)
(-3,1)
4
null
4
1
-999
(2,2)
(-1,1)
2
null
2
1
-999
(2,3)
(-1,1)
2
null
2
1
-999
(3,0)
(-1,0)
2.618034
null
1
1
1
(3,1)
(-2,-1)
2
null
2
1
-999
(2,-1)
(1,-1)
2
null
2
1
-999
(2,0)
(1,-1)
2
null
2
1
-999
(2,1)
(1,-1)
2
null
2
1
-999
(2,2)
(1,-1)
2
null
2
1
-999
(3,-3)
(-2,3)
2
null
2
1
-999
(3,-3)
(1,3)
0.5
null
-4
2
-999
(1,-1)
(-1,-1)
0.5
null
-4
2
-999
(3,-1)
(-1,-1)
0.25
null
-4
1
-999
(2,3)
(1,-1)
2
null
2
1
-999
(1,-3)
(2,-1)
0.5
null
-4
2
-999
(3,-2)
(2,-1)
4
null
4
1
-999
(1,0)
(2,-1)
2
null
2
1
-999
(2,0)
(3,-3)
2
null
2
1
-999
(2,2)
(3,-3)
2
null
2
1
-999
(2,3)
(3,-3)
2
null
2
1
-999
(2,-3)
(2,-2)
2
null
2
1
-999
(2,-2)
(2,-2)
2
null
2
1
-999
(2,-1)
(2,-2)
2
null
2
1
-999
(1,1)
(2,1)
2
null
2
1
-999
(2,-3)
(-2,2)
2
null
2
1
-999
(2,-2)
(-2,2)
2
null
2
1
-999
(2,-1)
(-2,2)
2
null
2
1
-999
(2,0)
(-2,2)
2
null
2
1
-999
(2,-3)
(-1,1)
2
null
2
1
-999
(2,-2)
(-1,1)
2
null
2
1
-999
(2,0)
(-1,1)
2
null
2
1
-999
(2,1)
(-1,1)
2
null
2
1
-999
(2,1)
(-2,2)
2
null
2
1
-999
(2,2)
(-2,2)
2
null
2
1
-999
(2,3)
(-2,2)
2
null
2
1
-999
(1,1)
(1,1)
1.718282
null
-1
1
1
(2,0)
(-3,3)
2
null
2
1
-999
(2,1)
(-3,3)
2
null
2
1
-999
(2,2)
(-3,3)
2
null
2
1
-999
(2,3)
(-3,3)
2
null
2
1
-999
(3,1)
(0,-1)
2.718282
null
0
1
1
(2,-3)
(1,-1)
2
null
2
1
-999
(2,-2)
(1,-1)
2
null
2
1
-999
(-3,0)
(-1,0)
-2.618034
null
-1
1
-1
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(1,0)
-1.618034
null
0
1
-1
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1.618034
null
0
1
1
(2,0)
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2.414214
null
1
1
1
(1,0)
(3,-1)
2
null
2
1
-999
(-2,2)
(3,-1)
2
null
2
1
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(-1,2)
(3,-1)
0.5
null
-4
2
-999
(-1,-1)
(1,1)
-1.718282
null
1
1
-1
(-3,1)
(1,1)
0.25
null
-4
1
-999
(-1,1)
(1,1)
0.5
null
-4
2
-999
(-2,0)
(1,0)
-2.414214
null
-1
1
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2
null
2
1
-999
(-3,-1)
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-2.718282
null
0
1
-1
(0,2)
(2,-1)
0.5
null
-4
2
-999
(1,0)
(2,0)
2
null
2
1
-999
(-2,2)
(-3,1)
2
null
2
1
-999
(0,-2)
(-2,1)
0.5
null
-4
2
-999
(1,-2)
(-2,1)
2
null
2
1
-999
(3,-2)
(-2,1)
2
null
2
1
-999
(7,2,2)
(-10,-10,-10)
2
null
2
1
-999
(4,5,5)
(-4,-10,-10)
2
null
2
1
-999
(6,5,5)
(-8,-10,-10)
4
null
4
1
-999
(4,-10,5)
(-4,-10,-10)
2
null
2
1
-999
(5,10,10)
(-4,-10,-10)
4
null
4
1
-999
(8,0,2)
(-5,-10,-10)
0.5
null
-4
2
-999
(3,10,10)
(-2,-10,-10)
2
null
2
1
-999
(1,-10,-10)
(2,-10,-10)
2
null
2
1
-999
(0,-5,-5)
(4,-10,-10)
2
null
2
1
-999
(3,-10,-10)
(4,-10,-10)
4
null
4
1
-999
(5,9,10)
(-4,-9,-10)
4
null
4
1
-999
(5,7,0)
(-2,-9,-10)
2
null
2
1
-999
(3,9,10)
(-2,-9,-10)
2
null
2
1
-999
(1,-9,-10)
(2,-9,-10)
2
null
2
1
-999
End of preview.

Ramanujan Machine — GPU Formula Discovery Results

GPU-accelerated search for new continued fraction formulas for mathematical constants, inspired by Raayoni et al. (2024). 586 billion candidates evaluated through degree 7 — zero confirmed transcendental formulas.

Part of the bigcompute.science project. AI-audited, not peer-reviewed.

Method

For polynomial pairs (P, Q) with bounded integer coefficients, evaluate the generalized continued fraction to double precision (500 terms), then match against 10 base constants + 29 compound expressions. v3 kernel filters degenerate zero-value matches.

Results

File Degree Range Candidates Real Hits Transcendental?
hits_deg1_range3.csv 1 [-3,3] 2,401 ~50 No
hits_deg2_range20.csv 2 [-20,20] 4.75B 4.49M No (sqrt(5) only)
hits_deg3_range10.csv 3 [-10,10] 37.8B 119M No
hits_deg4_range5.csv 4 [-5,5] 25.9B 260 No (2 false positive)
hits_deg5_range4.csv 5 [-4,4] 282B 284 No (4 false positive)
hits_deg6_range2.csv 6 [-2,2] 6.1B 2 No
hits_deg7_range2.csv 7 [-2,2] 153B 78.3K No (30 false positive)
Total ~586B Zero transcendental

Additional runs in results/ and data/ folders at intermediate ranges.

Key Finding

After 586 billion candidates (82,000x larger than Raayoni et al.), zero transcendental CF formulas were found using double-precision screening. All matches are algebraic (sqrt(2), sqrt(5), phi). 36 compound matches (pi/4, sqrt(pi), e/pi, etc.) all failed mpmath 50-digit verification — they are false positives inherent to the double-precision methodology.

Methodology limitation: Double-precision (53-bit) screening is insufficient for detecting transcendental CF formulas, which converge slowly. Raayoni et al. used arbitrary precision. A GPU PSLQ implementation is needed for the next phase.

Source

Citation 

@misc{humphreys2026ramanujan,
  author = {Humphreys, Cahlen and Claude (Anthropic)},
  title = {Ramanujan Machine: GPU-Accelerated CF Formula Discovery},
  year = {2026},
  publisher = {Hugging Face},
  url = {https://huggingface.co/datasets/cahlen/ramanujan-machine-results}
}

Human-AI collaborative work. AI-audited against published literature. Not independently peer-reviewed. CC BY 4.0.
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