I heard here that Collatz conjecture was checked at least for every first $5 \cdot 10^{18}$ natural numbers, but I cannot find any source or actual information about this. Can anyone help to find out up to which number (or factor of 10) we can now say that Collatz Conjecture is definitely true?
[Math] For how many consecutive numbers Collatz conjecture was checked
collatz conjecturecomputational mathematics
Best Answer
The following published paper gives $20\times 2^{58}\approx 5.7646\times 10^{18}$:
Tomás Oliveira e Silva, "Empirical Verification of the 3x+1 and Related Conjectures." In "The Ultimate Challenge: The 3x+1 Problem," (edited by Jeffrey C. Lagarias), pp. 189-207, American Mathematical Society, 2010.
The author's website suggests ongoing work, but the sublink is down.