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.

The first number of this zone (192252423729713) was found on August 12, 2016 by a Canadian programmer Andy Martin and is the 8th term of А275939. The full description of this zone (including its upper bound and number of terms) was not available before. This zone, together with the previously discovered by us 8th and 9th zone for ∆{4;3,1}(x), are the first 3 zones in Chebyshev’s bias for small dividers (4, 8, 12 и 24) discovered since 1996.

We are planning to register in OEIS two sequences describing this zone in the nearest future.