Collatz function data for 2^25964951 – 1 (#11 known megaprime)

We publish our first data on the Collatz function for 2^25964951 – 1 (#11 known megaprime) and two of its odd neighbors located at ±2. Continue reading

Collatz function data for 2^24036583 – 1 (#12 known megaprime)

We publish our first data on the Collatz function for 2^24036583 – 1 (#12 known megaprime) and two of its odd neighbors located at ±2. Continue reading

Collatz function data for 2^20996011 – 1 (#13 known megaprime)

We publish our first data on the Collatz function for 2^20996011 – 1 (#13 known megaprime) and two of its odd neighbors located at ±2. Continue reading

Collatz function data for 1059094^1048576 + 1 (#14 known megaprime)

We publish our first data on the Collatz function for 1059094^1048576 + 1 (#14 known megaprime) and two of its odd neighbors located at ±4. Continue reading

Collatz function data for 919444^1048576 + 1 (#15 known megaprime)

We publish our first data on the Collatz function for (919444^1048576 + 1 (#15 known megaprime) and two of its odd neighbors located at ±10. Continue reading

Collatz function data for (2^19375200)*168451 + 1 (#16 known megaprime)

We publish our first data on the Collatz function for (2^19375200)*168451 + 1 (#16 known megaprime) and its closest 2 odd neighbors. Continue reading

Collatz conjecture test for the Top 16 megaprimes started

We have started to test the Collatz conjecture for the Top 16 megaprimes as well as some of their selected odd neighbors. The results will be published in due course.

Breakthrough Junior Challenge 2019 Video: Chebyshev’s Bias

New 7th sign-changing zone for ∆{24;13,1}(x) in Chebyshev’s bias found

We found the 7th sign-changing zone for for ∆{24;13,1}(x) between 5*1015 and 1016. It starts with 8744052767229817, ends with 8772206355445549 and contains 410687 terms. The results are contributed into 2 OEIS sequences: A295355 and A295356.

Chebyshev’s Bias: 165 Years of History

Intel ISEF 2019 Video Presentation

Switch to multi-threading for Chebyshev’s bias software

We started to develop a new version of our “4000 Chebyshev’s Bias Tester” that uses OpenMP for multi-threading.

Initial tests indicated that the test speed could be increased 4-5 times on a 4-core 8-thread processor that launches 8 copies of primesieve as a real-time prime number generator.

With the advent of affordable multi-core processors such as 32-core 64-thread AMD Ryzen™ Threadripper™ 2990WX Processor, the ranges beyond 1016 become possible in reasonable time without supercomputers and massively parallel processing (MPP).

10^16 test range reached for Chebyshev’s bias

We successfully reached 1016 test range for Chebyshev’s bias.

All results will be published in our repository and contributed to OEIS  in due course.

EUCYS 2018 Presentation

01-A3 Presentation v7.3EN no

5*10^15 test range reached for Chebyshev’s bias

We successfully reached 5*1015 test range for Chebyshev’s bias.

All results will be published in our repository and contributed to OEIS  in due course.