Articles
All 15 entries →γ, the harmonic remainder
Take the first n reciprocals, subtract ln n; what survives is γ — and no one can prove it irrational.
NuclearPlane7879 min▲ 0▼ 0 ℵ1202 Difficulty25.9Apéry’s theorem
ζ(3) is irrational. Apéry’s 1978 proof is an integer race that the logarithm loses.
NuclearPlane78714 min▲ 1▼ 0 ℵ0078 Difficulty21.4Sixty-four bits of Ω
The halting probability is a definable real whose digits outrun every formal system. Here are 64 of them.
NuclearPlane78710 min▲ 0▼ 0 ℵ2314 Difficulty19.6Gelfond’s constant
e^π is transcendental by a two-line identity; π^e remains unclassified. Includes a famous near-integer.
NuclearPlane7878 min▲ 0▼ 0 ℵ1131 Difficulty17.3Random Fibonacci
Flip coins in the Fibonacci recurrence and it still grows exponentially — at Viswanath’s rate.
NuclearPlane7879 min▲ 0▼ 0 ℵ1902 Difficulty14.8Brun’s constant and a division bug
Twin-prime reciprocals converge to Brun’s constant; computing it exposed the Pentium’s divider.
NuclearPlane7878 min▲ 0▼ 0Announcements
Full record →AZMC Summer ‘26 enters the public registry as the first planned edition in the AZMC/AZIME answer-only contest series.
AZMC Summer ‘26 enters the public registry as the first planned edition in the AZMC/AZIME answer-only contest series.
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AlephZero enters development
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