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

On October 6, 2017, in addition to A051025, we published in Online Encyclopedia of Integer Sequences (OEIS) under A051024 the full data on the numbers of all 418933 primes where ∆{4;3,1}(x) becomes equal to -1. Staring from 27556th term equal to 316064952540 (that corresponds to the prime 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 actually found. Continue reading

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