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).

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.

Last Chebyshev’s bias data available in our repository

The last Chebyshev’s bias data became updated and available in our repository.

Chebyshev’s bias test range increased to 10^16

We further expanded Chebyshev’s bias test range 10 times to 1016. At the first stage, the tests will be run up to 5*1015. Expected time to complete the first stage – August, 2018.

Provisional 50th Mersenne prime M77232917 supports Collatz conjecture

On March 17th, 2018 our “3007 Collatz Tester for Mersenne Primes” (the improved version of “3000 Collatz Tester”) tested the provisional 50th Mersenne prime M77232917 for being in agreement with Collatz conjecture and supported it. Continue reading

Our research won “Mathematics and its applications in modern technologies” section of “Step Into The Future” science forum

Our research presentation “Testing Chebyshev’s bias for prime numbers up to 1015” became the only winner of the “Mathematics and its applications in modern technologies” section of “Step Into The Future” science forum that took place in Moscow on March 19-23, 2018. Continue reading

We participated in “Step Into The Future” science forum

Between March 19th and 23rd 2018 we participated in all-Russian science forum “Step Into The Future” with our research work “Testing Chebyshev’s Bias for prime numbers up to 1015 “.

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