Convergence verification of the Collatz problem

The convergence of all numbers below 0 × 2⁶⁰ (≈ 2^inf) has been verified. The work unit is 2^Apr numbers. On modern GPUs, verification of one work unit takes 5 seconds on average. All source codes are available on this GitHub repository.

Progress towards verifying all numbers below 1 × 2⁶⁰

Lowest incomplete: 0.0000 % (work unit [Thu × 2^Apr, all work units below are verified)
Lowest unassigned: 0.0000 % (work unit [Thu × 2^Apr, all work units below are assigned or even verified)

Project log

2019-09-04 started the project

2020-05-07 the convergence of all numbers below 2⁶⁸ is verified

2021-12-10 the convergence of all numbers below 2⁶⁹ is verified

2023-07-09 the convergence of all numbers below 2⁷⁰ is verified

2023-11-03 the convergence of all numbers below 1.5 × 2⁷⁰ is verified

2025-01-15 the convergence of all numbers below 2⁷¹ is verified

References

Barina, D. Convergence verification of the Collatz problem. J Supercomput 77, 2681–2688 (2021). https://doi.org/10.1007/s11227-020-03368-x

Barina, D. Improved verification limit for the convergence of the Collatz conjecture. J Supercomput 81, 810 (2025). https://doi.org/10.1007/s11227-025-07337-0

Generated: Thu, 30 Apr 2026 21:28:15 +0200

Convergence verification of the Collatz problem

Progress towards verifying all numbers below 1 × 2⁶⁰

Results

Project log

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References

Convergence verification of the Collatz problem

Progress towards verifying all numbers below 1 × 260

Results

Project log

Contact

References

Progress towards verifying all numbers below 1 × 2⁶⁰