Constants Registry

Mathematical constants appearing as identified limiting values in the CMF Atlas. Each entry includes a 30-digit precision value, irrationality status, and links to CMF entries targeting that constant.

10 constants JSON endpoint ↗ Release manifest ↗
Irrationality / transcendence status: ✓ proven_transcendental ✓ proven_irrational ? open_question – algebraic
Constant 30-digit value Series / formula Irrational Transcend. CMF entries
\(\zeta(3)\)
zeta3
1.202056903159594285399738161511\(\displaystyle\sum_{n=1}^\infty n^{-3}\)✓ proven_irrational?—
\(\pi\)
pi
3.141592653589793238462643383280\(4\sum_{n=0}^\infty\frac{(-1)^n}{2n+1}\)✓ proven_transc.T—
\(e\)
e
2.718281828459045235360287471353\(\sum_{n=0}^\infty\frac{1}{n!}\)✓ proven_transc.T—
\(\ln 2\)
ln2
0.693147180559945309417232121458\(\sum_{n=1}^\infty\frac{(-1)^{n+1}}{n}\)✓ proven_transc.T—
\(\zeta(2)=\pi^2/6\)
zeta2
1.644934066848226436472415166646\(\sum_{n=1}^\infty n^{-2}\)✓ proven_transc.T—
\(\zeta(5)\)
zeta5
1.036927755143369926331365486458\(\sum_{n=1}^\infty n^{-5}\)? open_question?—
\(G\)
catalan
0.915965594177219015054603514932\(\sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)^2}\)? open_question?—
\(\sqrt{2}\)
sqrt2
1.414213562373095048801688724210\(\sqrt{2}\)✓ proven_irrationalNo—
\(\pi/2\)
pi_half
1.570796326794896619231321691640\(\pi/2\)✓ proven_transc.T—
\(\pi/4\)
pi_quarter
0.785398163397448309615660845820\(\pi/4\)✓ proven_transc.T—
Notes on open problems

ζ(5) and Catalan's constant G are widely believed to be irrational and transcendental, but no proof exists as of 2026. They are among the most important open problems in analytic number theory.

CMF Hunter entries with unidentified limits are not listed here — they appear in the browse table with an empty primary_constant field. Many of these may converge to rational numbers; see the research disclaimer on the Sources page.

Values computed using mpmath at 30+ decimal digit precision. The constants registry is also available as a machine-readable JSON endpoint: GET /constants