EUCYS 2018 Video

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 – November, 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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“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

First sign-changing zones for ∆{24;19,1}(x) in Chebyshev’s bias found

On December 27, 2017 our “4000 Chebyshev Bias Tester” completed testing all primes up to 10*1014  and found 5 first and previously unknown sign-changing zones for ∆{24;19,1}(x), where the value of ∆{24;19,1}(x) equals to -1. Continue reading

First sign-changing zones for ∆{24;17,1}(x) in Chebyshev’s bias found

On December 27, 2017 our “4000 Chebyshev Bias Tester” completed testing all primes up to 10*1014  and found 3 first and previously unknown sign-changing zones for ∆{24;17,1}(x), where the value of ∆{24;17,1}(x) equals to -1. Continue reading

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

On December 20, 2017 our “4000 Chebyshev Bias Tester” completed testing all primes up to 10*1014  and found 5 new and previously unknown sign-changing zones for ∆{24;13,1}(x), where the value of ∆{24;13,1}(x) equals to -1. Continue reading

Data on first sign-changing zone for ∆{8;7,1}(x) in Chebyshev’s bias included into OEIS

As we reported before, on November 20, 2017 we submitted two our sequences for registration with OEIS. The sequences fully defined the first found sign-changing zone for ∆{8;7,1}(x) in Chebyshev’s bias. 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

First sign-changing zone for ∆{8;7,1}(x) in Chebyshev’s bias found

On November 10th, 2017 our “4000 Chebyshev Bias Tester” fully determined the first sign-changing zone for ∆{8;7,1}(x) in Chebyshev’s bias (where ∆{8;7,1}(x) is equal to -1).

This zone starts with the prime 192252423729713, includes 234937 terms and ends with the prime 192876135747311. Continue reading

Full data on all 8 zones with 0 values for ∆{4;3,1}(x) in Chebyshev’s bias published

Оn October 15, 2017 we published in Online Encyclopedia of Integer Sequences (OEIS) under  A007351 the full data on all 419467 primes where ∆{4;3,1}(x) is equal to zero. Staring from 27410th term equal to 9103362505753 the published sequence includes data on the 8th sign-changing zone, that was predicted back in 2001 by a group of American mathematicians, but was never actually found. Continue reading