New and unknown 9th sign-changing zone in Chebyshev’s bias for ∆{4;3,1}(x) found

On October 10th, 2017 our  “4000 Chebyshev Bias Tester”  completed testing all primes up to 10*1013  and found a new and previously unknown 9th sign-changing zone for ∆{4;3,1}(x), where the value of ∆{4;3,1}(x) equals to -1. Continue reading

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

On October 6, 2017 we published in Online Encyclopedia of Integer Sequences (OEIS) under A051025 the full data on all 418933 primes where ∆{4;3,1}(x) becomes equal to -1. Staring from 27556th term equal to 9103362505801 the published sequence includes data on the 8th negative zone, that was predicted back in 2001 by a group of American mathematicians, but was never found. Continue reading

8th sign-changing zone in Chebyshev’s bias for ∆{4;3,1}(x) found

On October 1st, 2017 our  “4000 Chebyshev Bias Tester”  completed testing all primes up to 10*1012  and found the 8th sign-changing zone for ∆{4;3,1}(x), predicted in 2001 by American mathematicians  Carter Bays, Kevin Ford, Richard H. Hudson and Michael Rubinstein to be around 9.318*1012 . Continue reading

Chebyshev’s bias testing started

On March 22, 2017 we started to test Chebyshev’s bias for remainders modulo 4 for all primes up to  10*1015. Continue reading