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).

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.

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 “.

Continue reading

“The Practical Realization of a Cryptographic System Based on One-Time Pads” (in Russian)

We are publishing the short presentation of our paper called “The Practical Realization of a Cryptographic System Based on One-Time Pads” (in Russian) that won the top award in the Computer Science section of the Intel-Avangard conference (the part of Intel ISEF) on February 22-25, 2018.

OTP 20180219 v3.0FINAL

Our cryptography presentation won the top award at Intel-Avangard conference

On February 25, 2018 our cryptography paper and presentation “On practical realization of one-time pad cryptographic system” won the top award in the Computer Science section at Intel-Avangard conference, which is a part of international Intel ISEF competition. Continue reading

All Chebyshev’s bias data available at our repository

February 01, 2018 we made all our data on Chebyshev’s bias available at our repository. Continue reading

Number of steps in Collatz sequence for Mersenne primes from 46th to 49th published in OEIS

On November 14, 2017 our data on number of steps in Collatz sequence for Mersenne primes with the provisional index from 46th to 49th were included in OEIS as a comment to A181777. Prior to this A181777 contained information up to the 45th Mersenne prime only. Continue reading

Number of steps in Collatz sequence for Mersenne primes available for download

The data on the number of steps to reach one in Collatz sequence for Mersenne primes from the 1st to 45th (the last with confirmed index) became available for download from OEIS (A181777). The full sequence from the 1st to 49th Mersenne prime (the last known as of today) could be downloaded from our repository.

We contunue to publish our results in due course.